Business Research Methods

LESSON - 1

INTRODUCTION TO BUSINESS RESEARCH METHODS

Research - Meaning - Types - Nature and scope of research - Problem formulation -statement of research objective - value and cost of information - Decision theory -Organizational structure of research - Research process - research designs - exploratory-Descriptive - Experimental research.

OBJECTIVE

To equip the students with the basic understanding of the research methodology andprovide an insight into the application of modern analytical tools and techniques for thepurpose of management decision making.

STRUCTURE

· Value of Business Research· Scope of Research· Types of Research· Structure of Research

LEARNING OBJECTIVES

· To understand the importance of business research as a management decisionmaking tool

· To define business research· To understand the difference between basic and applied research· To understand when business research in needed and when it should be

conducted· To identify various topics for business research.

INTRODUCTION

The task of business research is to generate accurate information for use in decisionmaking. The emphasis of business research is shifting the decision makers fromintuitive information that is based on own judgment and gathering information intosystematic and objective investigation.

DEFINITION

The business research is defined as the systematic and objective process of gathering,recording and analyzing data for aid in making business decisions. Literally, researchmeans to "search again". It connotes patient study and scientific investigation where inthe research takes more careful look to discover to know about the subject of study. The

data collected and analyzed are to be accurate, the research need to be very objective.Thus, the role of researcher is to be detached and impersonal rather than engaging inbiased attempt. This means without objectivity the research is useless. The definition isrestricted to take decision in the aspects of business alone. This generates and providesthe necessary qualitative and quantitative information upon which, as base, thedecisions are taken. This information reducing the uncertainly of decisions and reducesthe risk of making wrong decisions. However research should be an "aid" to managerialjudgment, not a substitute for it. There is more to management than research. Applyingresearch remains a managerial art.

The study of research methods provides with the knowledge and skills that need to solvethe problems and meet the challenges of the fast-paced decision making environment.There are two important factors stimulate an interest in scientific approach to decisionmaking:

1. The is an increased need for more and better information, and

2. The availability of technical tools to meet this need.

During the last decade, we have witnessed dramatic changes in the businessenvironment. These changes have created new knowledge needs for the manager toconsider when evaluating any decision. The trend toward complexity has increased therisk associated with business decision, making it more important to have soundinformation base. The following are the few reasons which makes the researcher tolookout for newer and better information based on which the decisions are taken:

· There are more variables to consider on every decision· More knowledge exists in every field of management· The quality and theory and models to explain the tactics and strategic results are

improving.· Better arrangement of information· Advancement in computer allowed to create better database.· The power and ease of use of today's computer have given to capability to analyze

the data to solve managerial problems

The development of scientific method in business research lags behind the similardevelopments in physical science research which is more rigorous and much moreadvanced. But business research is of recent origin and moreover the finding cannot bepatented that of physical science research. Business research normally deals with topicssuch as human attitudes, behavior and performance. Even with these hindrances,business research is making strides in the scientific arena. Hence, the managers who arenot proposed ior this scientific application in business research will be at severedisadvantage.

Value of Business Research

The prime value of business research is that it reduces uncertainty by providinginformation that improves decision making process. The decision making process isassociated with the development and implementation of a strategy, which involves thefollowing

1. Identifying problems or opportunities

Before any strategy can be developed, an organization must determine where it wants togo and how it will get there. Business research can help managers to plan strategies bydetermining the nature of situations or by identifying the existence of problems ofopportunities that are present in the organization. Business research may be used as ascanning activity to provide information about what business happening or itsenvironment. Once it defines and indicates problems and opportunities, managers mayevaluate alternatives very easily and clear enough to make a decision.

2. Diagnosing and Assessing problems and opportunities

The important aspect of business research is the provision of diagnostic informationthat clarifies the situation. It there is a problem, they need to specify what happened andwhy. If an opportunity exists, they need to explore, clarify and refine the nature ofopportunity. This will help in developing alternative courses of action that are practical.

3. Selecting and implementing a course of action

After the alternative course of action has been clearly identified, business research isconducted to obtain scientific information which will aid in evaluating the alternativesand selecting the best course of action.

Need for Research

When a manager faced with two or more possible course if action, the researchercarefully need to take decision whether or not to conduct the research. The following arethe determinants.

1. Time Constraints

In most of the business environment, the decisions most must be made immediately,but conducting research systematically takes time. There will not be much time to relayon research. As a consequence, the decisions are sometimes made without adequateinformation and through understanding of the situation.

2. Availability of Data

Often managers possess enough information with no research. When they lack adequateinformation, research must be considered. The managers should think whether theresearch will be able to generate information needed to answer the basic question aboutwhich the decision is to be taken.

3. Nature of Information

The value of research will depend upon the nature of decisions to be made. A routinedecision does not require substantial information or warrants. However, for importantand strategic decision, more likely research needs to be conducted.

4. Benefits vs. Costs

The decision to conduct research boils down to these important questions.

1. Will the rate of return be worth the investment?

2. Will the information improve the quality of the decision?

3. Is the research expenditure the best use of available funds?

Thus, the cost of information should not exceed the benefits i.e. value of information.

What is Good Research?

Good research generates dependable data can be used reliable for making managerialdecisions. The following are the tips of good research.

· Purpose clearly defined, i.e., understanding problems clearly· The process described in sufficient details· The design carefully planned to yield results· Careful consideration must be given and maintain high ethical standards· Limitations properly revealed· Adequate analysis of the data and appropriate tools used· Presentation of data should be comprehensive, early understood and presented

unambiguously· Conclusion should base on the data obtained and justified.

Scope of Research

The scope of research on management is limited to business. A researcher conductingresearch within an organization may be referred as a "marketing researcher" or"organizational researcher", although business research is specialized and the termencompasses all the functional areas – Production, Finance, Marketing, HR etc. Thedifferent functional areas may investigate different phenomenon, but they arecomparable to one another because they use similar research methods. There are manykinds of areas are resembled in the business environment like forecasting, trendsenvironment, capital formation, portfolio analysis, cost analysis, risk analysis, TQM, jobsatisfaction, organizational effectiveness, climate, culture, market potential,segmentation, sales analysis, distribution channel, computer information needsanalysis, social values and establish and etc.

Types of Research

Research is to develop and evaluate concepts and theories. In broader sense researchcan be classified as.

1) Basic Research or Pure Research

It does not directly involve the solution to a particular problem. Although basic researchgenerally cannot be implemented, this is conducted to verify the acceptability of a giventheory or to discuss more about a certain concept.

2) Applied Research

It is conducted when a decision must be made about a specific real-life problem. Itencompasses those studies undertaken to answer question to specific problems or tomake decision about particular course of action.

However, the procedures and techniques utilized by both researchers do not differsubstantially. Both employ scientific method to answer questions. Broadly, the scientificmethod refers to techniques and procedures that help researcher to know andunderstand business phenomenon. The scientific method requires systematic analysisand logical interpretation of empirical evidence (facts from observation orexperimentation) to confirm or dispose prior conceptions. In basic research, it first teststhe prior conceptions or assumptions or hypothesis and then makes inferences andconclusions. In the applied research the use of scientific method assures objectivity ingathering facts and taking decision.

At the outset, it may be noted that there are several ways of studying and tackling aproblem. There is no single perfect design. Research designs have been classified byauthors in different ways. Different types of research designs have emerged on theaccount of the different perspectives from which the problem or opportunity is viewed.However, the research designs broadly classified into three categories - exploratory,descriptive, and causal research. The research can be classified on the basis of eithertechnique or function. Experiment, surveys and observation are few commontechniques. The technique may be qualitative of quantitative. Based on the nature of theproblems or purpose of study the above three are used invariably used in managementparlance.

3) Exploratory Research

The focus is mainly on discovering of ideas. An exploratory research is generally basedon secondary data that are already available. It is to be understood that this type ofstudy is conducted to classify ambiguous problems. These studies provide informationto use in analyzing situations. This will helps to crystallize a problem and identifyinformation needs for further research. The purpose of exploration is usually to develophypotheses or question for further research. The exploration may be accomplished withdifferent techniques. Both qualitative and quantitative techniques are applicable

although exploration studies relies on more heavily a qualitative technique likeexperience survey, focus group.

4) Descriptive Research

The major purpose is to describe characteristics of a population or phenomenon.Descriptive research seeks to determine to answers to who, what, when, where and howquestions. Unlike explorative, these studies are based on some previous understandingof the nature of the research problem. Descriptive studies can be divided into two broadcategories-Cross sectional and Longitudinal. The former type is more frequently used. Across section study is concerned with the sample of elements from a given population. Itis carried out once and represents one point at time. The longitudinal studies are basedon panel data or panel methods. A panel is sample of representatives who areinterviewed and then re-interviewed from time to time, that is, longitudinal studies arerepeated over an extended period.

5) Causal Research

The main goal of causal research is the identify cause and effect relationship amongvariables. It attempts to establish that when we do one thing what another thing willhappen. Normally explorative and descriptive studies precede causal research.

However, based on the breadth and depth of study, another method is frequently used ismanagement called case study research. This places more emphasis on a full contextualanalysis of fever events or conditions and their interrelations. An emphasis on detailsprovides valuable insight for problem solving, evaluation and strategy. The detail isgathered from multiple sources of information.

Value of Information and Cost

Over the part decade many cultural, technological are competitive factors have created avariety of new challenges, problems and opportunities for today's decision makers inbusiness. First, the rapid advances in interactive marketing communicationtechnologies have increased the need for database management skills. Moreover,advancements associated with the so called information super high ways have createdgreater emphasis on secondary data collection, analysis and interpretation. Second,there is a growing movement emphasizes quality improvements. This placed moreimportance on cross sectional information then over before. Third is the expansion ofglobal markets which introduces a new set of multicultural problem and question.

These three factors that influence the research process and it take steps into seeking newinformation in management perspective. There may be situations where management issufficiently clear that no additional information is likely to change its decision. In suchcases, it is obvious that the value of information is negligible. In contrast, there aresituations where the decisions look out for information which is not available easily.Unless the information collected does not led to change or modify a decision, theinformation has no value. Generally information is most valuable in cases i) where there

is unsure of what is to be done and ii) where extreme profits or losses involved. Apertinent question is-how much information should be collected in a given situation?Since the collected information involves a cost, it is necessary to ensure that the benefitfrom the information is more than the cost involved in its collection.

Decision Theory

With reference to the above discussion, an attempt is needed to see how information canbe evaluated for setting up a limit. The concept of probability is the basis of decisionmaker under conditions of uncertainly. These are three basic sources of assigningprobabilities

1) Based on a logic / deduction: For e.g., when a coin is tossed, the probability ofgetting a head or tail is 0.5.

2) Past experience / Empirical evidence: The experience gained in the processresolving these problems in the past. On the basis of its past experience, it may be in abetter positive to estimate the probability of new decisions.

3) Subjective Estimate: The most frequently used method, it is based on theknowledge and information with respect to researcher for the probability estimates.

The above discussion was confined to single stage problem wherein the researcher isrequired to select the best course of action on the basis of information available at apoint at time. However, there are problems with multiple stages wherein a sequence ofdecisions involved. Each decision leads to a chance event which in turn influences thenext decision. In those cases, a Decision Tree Analysis i.e. graphical derives depictingthe sequence of action-event combination, will be useful in making a choice between twoalternatives. If the decision tree is not helpful, more sophisticated technological knownas Bayesian Analysis can be used. Here, the probabilities can be revised on account ofthe availability of new information using prior, posterior and pre-posterior analysis.

There is a great deal between budgeting and value assessment in management decisionto conduct research. An appropriate research study should help managers avoid lossesand increase sales or profits; otherwise, research can be wasteful. The decision makerwants a cost-estimate for a research project and equally precise assurance that usefulinformation will result from the research. Even if the researcher can give good cost andinformation estimates, the decision maker or manager still must judge whether thebenefits out-weigh the costs.

Conceptually, the value of research information is not difficult to determine. In businesssituation the research should provide added revenues or reduce expenses. The value ofresearch information may be judge in terms of “the difference between the results ofdecisions made with the information and the result that would be made without it”. It issimple to state, in actual application, it presents difficult measurement problems.

Guideline for approximately the cost-to-value of Research

1. Focus on the most important issues of the project: Identify certain issues asimportant and others as peripheral to the problems. Unimportant issues are only todrain resources.

2. Never try to do much: There is limit to the amount of information that can becollected. The researcher must take a trade-off between the number of issues that can bedealt with the depth of each issue. Therefore it is necessary to focus on those issues ofgreatest potential value.

3. Determine whether secondary, primary information or combination isneeded: The most appropriate must be selected that should address the statedproblem.

4. Analyze all potential methods of collecting information: Alternative datasources and research designs are available that will allow detailed investigation of issuesat a relatively low cost.

5. Subjectively asses the value of information: The researcher need to ask somefundamental questions relating to objections. For example, a) Can the information becollected at all? b) Can the information tell something more that already what we have?c) Will the information provide significant insights? d) What benefits will be deliveredfrom this information?

Structure of Research

Business research can take many forms, but systematic inquiry is a common thread.Systematic inquiry requires an orderly investigation. Business research is a sequence ofhighly interrelated activity. The steps research process overlap continuously.Nevertheless, research on management often follows a general pattern. The styles are:

1. Defining the problem

2. Planning a research design

3. Planning a sample

4. Collecting data

5. Analyzing the data

6. Formulating the conclusions and preparing the report

SUMMARY

This paper outlined the importance of business research. Difference between basic andapplied research have been dealt in detail. This chapter has given the meaning, scope,types, and structure of the research.

KEY TERMS

· Research· Value of research· Need for research· Good Research· Scope of research· Types of research· Basic research· Applied research· Scientific method· Exploratory research· Descriptive research· Cross - sectional and longitudinal· Causal research· Decision theory· Structure

QUESTIONS

1. What are some examples of business research in your particular field of interest?

2. What do you mean by research? Explain its significance in modem times.

3. What is the difference between applied and basic research?

4. What is good research?

5. Discuss: Explorative, descriptive and causal research.

6. Discuss the value of information and cost using decision theory.

7. Discuss the structure of business research.

- End of Chapter -

LESSON - 2

PROBLEM DEFINITION

OBJECTIVES

· To discuss the nature of decision makers objectives and the role they play indefining the research

· To understand that proper problem definition is essential for effective businessresearch

· To discuss the influence of the statement of the business problem on the specificresearch objectives

· To state research problem in terms of clear and precise research objectives.

STRUCTURE

· Problem definition· Situation analysis· Measurable Symptoms· Unit of analysis· Hypothesis and Research objectives

PROBLEM DEFINITION

Before choosing a research design, manager and researcher need a sense of direction forthe investigation. It is extremely important to define the business problem carefullybecause the definition determines the purposes of the research and ultimately theresearch design. Well defined problem is half solved problems - hence, researcher mustunderstand how to define problem. The formal quantitative research process should notbegin until the problem has been clearly defined. Determination of research problemconsists of three important tasks namely,

1. Classifying in argument information needs.2. Redefining research problem, and3. Establishing hypothesis & research objectives.

Step 1: To ensure that appropriate information created through this process, researchermust assist decision maker in making sure that the problem or opportunity has beenclearly defined and the decision maker is aware of the information requirements. Thisinclude the following activities namely,

i) Purpose: Here, the decision maker holds the responsibility of addressing arecognized decision problem or opportunity. The researcher begins the process byasking the decision maker to express his or her reasons for thinking there is a need toundertake research. By this questioning process, the researcher can develop insights aswhat they believe to be the problems. One method that might be employed to familiarizethe decision maker is the iceberg principle. The dangerous part of many problems,like submersed portion of the iceberg, is neither visible nor understood by managers. Ifthe submerged position of the problem is omitted from the problem definition, thenresult may be less than optimal.

ii) Situation Analysis or understanding the situation: To gain the completeunderstanding, both should perform a basic situation analysis of the circumstances

surrounding the problem area. A situational analysis is a popular tool that focuses onthe informal gathering of background information to familiarize the overall complexityof the decision. A situation analysis attempts to identify the event and factors that haveled to the current decision problem situation. To objectively understand the client'sdomain (i.e., industry, competition, product line, markets etc) the researchers not relyonly on the information provided by client but also others. In short the researcher mustdevelop expertise in the client's business.

iii) Identifying and separating measurable symptoms: Once the researcherunderstands the overall problem situation, they must work with decision maker toseparate the problems from the observable and measurable symptoms that may havebeen initially perceived as the being the decision problem.

iv) Determining unit of analysis: The researcher must be able to specify whetherdata should be collected about individual, households, organizations, departments,geographical areas, specific object or some contributions of these. The unit of analysiswill provide direction in later activities such as scale measurement development anddrawing appropriate sample of respondents.

v) Determining relevant variables: Here, the focus is on the identifying thedifferent independent or dependent variables. It is determination of type of information(i.e., facts, estimates, predictions, relationships) and specific constructs (i.e. concepts orideas about an object, attributes, or phenomenon that are worth measurement)

Step 2:

Once the problem is understood and specific information requirements are identified,then the researcher must redefine the problem in more specific terms. In reframing theproblems and questions as information research questions, they must use their scientificknowledge expertise. Establishing research questions specific to problems will force thedecision maker to provide additional information that is relevant to the actual problems.In other situations, redefining problems as research problems can lead to theestablishment of research hypothesis rather than questions.

Step 3: (Hypothesis & Research objective)

A hypothesis is basically an unproven started of a research question in a testableformat. Hypothetical statement can be formulated about any variable and can express apossible relationship between two or more variables. While research questions andhypotheses are similar in their intent to express relationship, the hypotheses tend to bemore specific and declarative, whereas research questions are more interrogative. Inother words hypotheses are statement that can be empirically tested.

Research objectives are precise statements of what a research project will attempt toachieve. It indirectly represents a blueprint of research activities. Research objectivesallow the researcher to document concise, measurable and realistic events that eitherincrease or decrease the magnitude of management problems. More importantly it

allows for the specification of information required to assist management decisionmaking capabilities.

SUMMARY

Nature of decision maker’s objectives, and the role they play in defining the researchhave been dealt in detail. This chapter has given the steps involved in defining theproblem.

KEY TERMS

· Problem definition· Iceberg principle· Situation analysis· Unit of analysis· Variables· Hypotheses· Research objectives

QUESTIONS

1. What is the task of problem definition?

2. What is the iceberg principle?

3. State a problem in your field of interest, and list some variables that might beinvestigated to solve this problem.

4. What do you mean by hypothesis?

5. What is a research objective?

- End of Chapter -

LESSON – 3

RESEARCH PROCESS AND DESIGN

OBJECTIVES

· To list the stages in the business research process· To identify and briefly discuss the various decision alternatives available to the

researcher during each stage of the research process.

· To classify business research as exploratory, descriptive, and causal research· To discuss categories of research under exploratory, descriptive and causal

research.

STRUCTURE

· Research process· Research design· Types of research designs· Explorative research· Descriptive research· Casual research

Research Process

Before discussing the phases and specific steps of research process, it is important toemphasize the need for information and when the research is conducted or not. In thiscontext, the research process may be called as information research process that wouldbe more appropriate in business parlance. The information research is used to reflectthe evolving changes occurring within the management and the rapid changes facingmany decision makers regarding how firms conduct both internal and externalactivities. Hence, understanding the process of transforming raw data into usableinformation from broader information and expanding the applicability of the researchprocess in solving business problems and opportunities is very important.

Overview: The research process has been described anywhere from 6 to 11standardized stages. Here, the process consist of four distinct inter related phases thathave logical, hierarchical ordering depicted below.

Diagram: Four phases of Research Process

However, each phase should be viewed as a separate process that consists ofcombination of integrated steps and specific procedures. The four phases andcorresponding step guided by the principles of scientific method, which involvesformalized research procedures that can be characterized as logical, objective,systematic, reliable, valid and ongoing.

Integrative steps within research process

The following exhibit represents the interrelated steps of the 4 phases of the researchprocess. Generally researchers should follow the steps in order. However, thecomplexity of the problem, the level of risk involved and management needs willdetermine the order of the process.

Exhibit

Phase 1: Determination of Research Problem

Step 1: Determining management information needs

Step 2: Redefining the decision problem as research problem.

Step 3: Establishing research objectives.

Phase 2: Development of Research Design

Step 4: Determining to evaluate research design.

Step 5: Determining the data source.

Step 6: Determining the sample plan and sample size.

Step 7: Determining the measurement scales.

Phase 3: Execution of the Research Design

Step 8: Data collection and processing data.

Step 9: Analysing the data.

Phase 4: Communication of the Results

Step 10: Preparing and presenting the final report to management.

Step 1: Determining management information needs

Before the researcher becomes involved usually, the decision maker has to make aformal statement of what they believe is the issue. At this point, the researcher'sresponsibility is to make sure management has clearly and correctly specified theopportunity or question. It is important for the decision maker and the researcher toagree on the definition of the problem so that the result of the research process willproduce useful information. Actually the researcher should assist the decision maker indetermining whether the referred problem is really a problem or just a symptom or a yetunidentified problem. Finally the researchers list the factors that could have a direct orindirect impact on the defined problem or opportunity.

Step 2: Redefining the decision problem as research problem.

Once the researcher and decision makers have identified the specific information needs,the researcher must redefine the problem in scientific terms since the researcher feelmore comfortable using a scientific framework. This is very critical because, it influencesmany other steps. It is the researcher's responsibility to state the initial variablesassociated with the problem in the form of one or more question formats (how, what,where, when or why). In addition, the researcher need to focus on determining whatspecific information is required (i.e., facts, estimates, predictions, relationships or somecombination) and also of quality of information which includes the value of information.

Step 3: Establishing research objectives.

The research objective should follow from the definition of research problem establishedin Step 2. Formally stated objective provides the guidelines for determining other stepsto be undertaken. The undertaking assumption is that, if the objectives are achieved, thedecision maker will have information to solve the problem.

Step 4: Determining to evaluate research design.

The research design serves as a master plan of methods and procedures that should beused to collect and analyze the data needed by the decision maker. In this master plan,the researcher must consider the design technique (survey, observation, andexperiment), the sampling methodology and procedures, the schedule and the budget.Although every problem is unique, but most of the objectives can be met using one ofthree types of research designs: exploratory, descriptive, and casual. Exploratory focuseson collecting either secondary or primary data and using unstructured formal orinformal procedures to interpret them. It is often used simply classify problems oropportunity and it is not intended to provide conclusive information. Some examples ofexploratory studies are focus group interview, expensive surveys and pilot studies.Descriptive studies that describe the existing characteristic which generally allows todraw inference and can lead to a course of action. Causal studies are designed to collectinformation about cause and effect relationship between two or more variables.

Step 5: Determining the data source.

This can be classified as being either secondary or primary. Secondary data can usuallybe gathered faster and at less cost than primary data. Secondary data are historical datapreviously collected and assembled for some research problem other than the currentsituation. In contrast primary data represent firsthand data, and yet to have meaningfulinterpretation and it employs either surveyor observation.

Step 6: Determining the sample plan and sample size.

To make inference or prediction about any phenomenon we need to understand whereor who is supplying the raw data and how representative those data are. Therefore,researchers need to identify the relevant defined target population. The researcher can

choose between a sample (small population) and census (entire population). To achievethis research objective, the researcher needs to develop explicit sampling plan which willserve as a blueprint for defining the target population. Sampling plans can be classifiedinto two general types: probability (equal chance) and non probability. Since samplingsize affects quality and general ability, researchers, must think carefully about howmany people to include or how many objects to investigate.

Step 7: Determining the measurement scales.

This step focuses on determining the dimensions of the factors being investigated andmeasuring the variables that underlie the defined problem. This determines how muchraw data can be collected and the amount of data to be collected. The level ofinformation (nominal, ordinal, interval, and ratios), the reliability, the validity anddimension (uni vs. multi) will determine the measurement process.

Step 8: Data collection and processing data.

There are two fundamental approaches to gather raw data. One is to ask questions aboutvariables and phenomena using trained interviewers or questionnaires. The other is toobserve variables or phenomena using professional observers or high tech mechanicaldevices. Self - administered surveys, personal interviews, computer simulations,telephone interviews are some of the tools to collect data. The questioning allows awider variety of collective of data about not only past, present but also the state of mindor intentions. Observation can be characterized as natural, contrived, disguised orundisguised, structured or unstructured, direct or indirect, human or mechanical, anduses the devices like video camera, tape recorders, audiometer, eye camera, psycho-galvanometer or pupil meter. After the raw data collected, a coding scheme is needed sothat the raw data can be entered into computers. It is assigning logical numericaldescription to all response categories. The researcher must then clean the raw data ofeither coding or data entry error.

Step 9: Analysing the data.

Using a variety of data analysis technique, the researcher can create new, complex datastructure by continuing two or more variables into indexes, ratios, constructs and so on.Analysis can vary from simple frequency distribution (percentage) to sample statisticmeasures (mode, median, mean, standard deviation, and standard error) to multivariatedata analysis.

Step 10: Preparing and presenting the final report to management.

This step is to prepare and present the final research report to management. The reportshould contain executive summary, introduction, problem definition and objectives,methodology, analysis, results and finding, finally suggestions and recommendation. Italso includes appendix. Any researcher is expected not only submit well producedwritten report but also oral presentation.

Research Design

Kerlinger, in his "Foundations of Behavioral Research" book defines, "Research designis the plan structure, and strategy of investigation conceived so as to obtain answers toresearch questions and to control variance". The plan is overall scheme or program ofthe research. It includes an outline of what the investigator will do from writinghypotheses and their operational implication to the final analysis of data. A structure isthe framework, and the relations among variables of a study. According to Green & Tull,a research design is the specification of methods and procedures for acquiring theinformation needed. It is the overall operational pattern or framework of the projectthat stipulates what information is to be collected from which sources by whatprocedures.

From the above definitions it can be understood that the research design is more or lessa blueprint of research, which lays down the methods and procedure for requisitecollection of information and measurement and analysis with a view to arrive atmeaningful conclusions of the proposed study.

Types of Research Design

The different types of design are explained in the previous section (refer types ofresearch). There are three frequently used classification is give below.

I. Explorative

II. Descriptive

III. Casual

Here the focus will be how these studies are conducted and methods are explained:

I. Categories of Explorative Research

There are four general categories of explorative research methods. Each categoryprovides various alternative ways of getting information.

1. Experience Surveys

It is an attempt to discuss issues and ideas with top executive and knowledgepeople who have experience in the field. This research in the form of experiencesurvey may be quite informal. This activity intends only to get ideas about the'problems. Often an experience survey may consist of interviews with a smallnumber of people who have been carefully selected. The respondents willgenerally be allowed to discuss the questions with few constraints. Hence, thepurpose of such experts is to help formulate the problem and classify conceptsrather than develop conclusive evidence.

2. Secondary Data Analysis

Another quick source of background information is trade literature. Usingsecondary data may equally important to applied research. Investigating datethat has been completed for some purpose other than the present one is one ofthe frequent forms of exploratory research. Also, it is to remember that thismethod often used in descriptive analysis.

3. Case Studies

It is to obtain information one or few situation that are similar to the present one.The primary advantage of case study is that entire entity can be investigated indepth and with meticulous attention in details. The results from this type shouldbe seen as tentative. Generalizing from a few cases can be dangerous, becausemore situations are not typical in same sense. But even if situations are notdirectly comparable, a number of insights can be gained and hypothesissuggested for future research.

4. Pilot Studies

In the context of exploratory research, a pilot study implies that some aspect ofthe research will be on a small scale. This generates primary data usually forqualitative analysis. The major categories are discussed below:

a. Focus Group Interview

The popular method in the qualitative research is an unstructured free-flowinginterview with a small group of people. It is not rigid, but flexible promote thatencourages discussions. The primary advantages are that they are relatively brief,easy to execute, quickly analyzed and inexpensive. However, a small group willrarely be a representative sample, no matter how carefully it is selected.

b. Projective Techniques

It is an indirect means of questioning that enable the respondent to projectbeliefs and feeling onto a third party, an inanimate object or a situation.Respondents are not required to provide answer to a structural format. They areencouraged to describe a situation in their own words, with little prompting bythe researcher, within the context of their own experiences, attitudes, personalityand to express opinions and emotions. The most common techniques are usedassociations, sentence completion, Thematic Apperception Test (TAT) and roleplaying.

c. Depth interview

It is similar to focus group but in the interviewing session the researcher asksmany questions and probes for elaboration. Here the role of researcher

(interviewers) is more important. He must be highly skillful who can influencerespondents to talk freely without disturbing the direction. It may last morehours, hence it is expensive.

II. Categories of Descriptive Research

In contrast to exploratory, descriptive studies are more formalized and typicallystructured with clearly stated hypothesis. When the researcher interested in knowingthe characteristics of certain groups such as age, sex, educational level, occupation orincome, a descriptive study may be necessary. Descriptive studies can be divided intotwo broad categories - cross sectional and longitudinal. The following are the methodsused in descriptive studies:

1. Secondary Data Analysis

2. Primary Data Analysis

3. Case studies

Several methods are available to collecting the information (i.e., observation,questionnaire, and examination of records with the merits and limitations, theresearcher may use one or more of these methods which have been discussed in detailsin later chapters. Thus the descriptive studies methods must be selected keeping in viewthe objectives of the study and the resources available. The said design can beappropriately referred to as a survey design using observing or questioning process, lit.

III. Categories of Causal Research

As the name implies, a causal design investigates the cause and effect relationshipbetween two or more variables. The causal studies may be classified as informal andformal or quasi / true and complex designs. The methods used in experimental researchare discussed hereunder:

1. The one-shot case study (after-only design)

2. Before-after without control group.

3. After-only with control group.

4. Before-after with one control group

5. Four-group, Six- study design (Solomon four group design)

6. Time series design

7. Completely randomized design

8. Randomized block design.

9. Factorial design

10. Latin square design

The first two methods are called as quasi experimental designs, next 3 methods arecalled as true experimental designs and last 4 methods are called complex designs. Inthis experimental design the following symbols are used in describing the variousexperimental designs:

X = Exposure of a group to an experimental treatment.

O = Observation or measurement of the dependent variable.

1. The one-shot case study design (after only design): The one-shotdesign, there should be a measure of what would happen when test units were notexposed to X to compare with the measure when subjects were exposed to X. Thisis diagrammed as follows:

X O1

2. Before - after without control group design: In this, the researcher islikely to conclude that the difference between O2 and O1 (O2 – O1) is the measure ofthe influence of the experimental treatment. The design is as follows:

O1 X O2

3. After only with control group design: The diagram is as follows:

Experimental Group: X O1

Control Group: X O2

The design is to randomly selected subjects and randomly assign to experimentalor the control group. The treatment is then measured in both groups at same time.The effect is calculated as follows:

O2 - O1

4. Before-after with one control group design: This is explained as follows:

Experimental Group: O1 X O2

Control Group: O3 X O4

As the diagram above indicated, the subjects of the experimental group are testedbefore and after being exposed to the treatment. The control group is tested twice,at the same time of experimental group, but these subjects are not exposed to thetreatment. The effect is calculated as follows:

(O2 - O1) - (O4 – O3)

5. Four-group, six- study design: (Solomon four groups design) Combining,the before - after with control group design and the after-only with control groupdesign provides a means for controlling testing affects, as well as other sources ofextraneous variations. The diagram as follows:

Experimental Group 1 O1 X O2

Control Group 1 O3 X O4

Experimental Group 2: X O5

Control Group 2: X O6

6. Time series design: When experiments are conducted over long periods oftime, they are more vulnerable to history effects due to changes in population,attitudes, economic patterns and the like. Hence, this is also called quasi-experimental design. This design can be diagrammed as follows:

O1 O2 O3 X O4 O5 O6

Several observations have been taken before and after the treatment to determinethe patterns after the treatment are similar to the pattern of before the treatments.

7. Completely randomized design (CRD): CRD is an experimental designthat uses a random process to assign experimental units to treatments. Here,randomization of experimental units to control extraneous variables whilemanipulating a single independent variable, the treatment variable.

8. Randomized block design (RBD): The RBD is an extension of the CRD. Aform of randomization is utilized to control for most extraneous variation. Here anattempt is made to isolate the effects of the single variable by blocking its effects.

9. Factorial design: A FD allows for testing the effects of two or moretreatment (factors) at various levels. It allows for the simultaneous manipulationof 2 or more variable at various levels. This design will measure main effect (i.e.,the influence on the dependent variable by each independent variable and alsointeraction effect.

10. Latin Square Design (LSD): The LSD attempts to control or block out theeffect of two or more confounding extraneous factors. This design is so namedbecause of the layout of the table that represents the design.

SUMMARY

This chapter has outlined the stages in business research prawn. Various types ofresearch design have been dealt in detail.

KEY TERMS

· Exploratory research· Descriptive research· Causal research· Focus group· Projective techniques· Case studies· Depth Interview· Experimental designs· Quasi experimental design· True experimental designs· Complex designs

QUESTIONS

1. Explain the different phases of research process.

2. Briefly describe the different steps involved in a research process.

3. What are major types researches in business?

4. Discuss the categories of exploratory and descriptive research.

5. Explain different experimental designs.

REFERENCES

1. Bellenger and et al, Marketing Research, Home Wood Illinois, Inc. 1978.

2. Boot, John C.G. and Cox., Edwin B., Statistical Analysis for Managerial Decisions, 2nded. New Delhi: McGraw Hill Publishing Co. Ltd.

3. Edwards, Allen, Statistical Methods, 2nd ed., New York. 1967.

- End of Chapter -

LESSON – 4

INTRODUCTION TO STATISTICS AND POPULATION PARAMETERS

OBJECTIVES

· Meaning and definition of Statistics· Nature of Statistical study· Importance of Statistics in business and also its limitations

STRUCTURE

· Nature of statistical study· Importance of statistics in business· Statistical quality control method· Limitation of statistics

INTRODUCTION

At the outset, it may be noted that the word 'Statistics' is used rather curiously in twosenses-plural and singular. In the plural sense, it refers to a set of figures. Thus, wespeak of production and sale of textiles, television sets, and so on. In the singular sense,Statistics refers to the whole body of analytical tools that are used to collect the figures,organize and interpret them and, finally, to draw conclusions from them.

It should be noted that both the aspects of Statistics are important if the quantitativedata are to serve their purpose. If Statistics, as a subject, is inadequate and consists ofpoor methodology, we would not know the right procedure to extract from the data theinformation they contain. On the other hand, if our figures are defective in the sensethat they are inadequate or inaccurate, we would not reach the right conclusions eventhough our subject is well developed. With this brief introduction, let us first see howStatistics has been defined.

Statistics has been defined by various authors differently. In the initial period the role ofStatistics was confined to a few activities. As such, most of the experts gave a narrowdefinition of it. However, over a long period of time as its role gradually expanded,Statistics came to be considered as much wider in its scope and, accordingly, the expertsgave a wider definition of it.

Spiegal, for instance, defines Statistics, highlighting its role in decision-makingparticularly under uncertainty, as follows:

"Statistics is concerned with scientific method for collecting, organising, summarising,presenting and analysing data as well as drawing valid conclusions and makingreasonable decisions on the basis of such analysis."

This definition covers all the aspects and then tries to link them up with decision-making. After all, Statistics as a subject must help one to reach a reasonable andappropriate decision on the basis of the analysis of numerical data collected earlier.

Using the term 'Statistics' in the plural sense, Secrist defines Statistics as

"Aggregate of facts, affected to a marked extent by multiplicity of causes, numericallyexpressed, enumerated or estimated according to reasonable standards of accuracy,collected in a systematic manner for a predetermined purpose, and placed in relation toeach other".

This definition of Secrist highlights a few major characteristics of statistics as givenbelow:

1. Statistics are aggregates of facts. This means that a single figure is not statistics.

2. Statistics are affected by a number of factors. For example, sale of a product dependson a number of factors such as its price, quality, competition, the income of theconsumers, and so on.

3. Statistics must be reasonably accurate. Wrong figures, if analysed, will lead toerroneous conclusions. Hence, it is necessary that conclusions must be based onaccurate figures.

4. Statistics must be collected in a systematic manner. If data are collected in ahaphazard manner, they will not be reliable and will lead to misleading conclusions.

5. Finally, statistics should be placed in relation to each other. If one collects dataunrelated to each other, then such data will be confusing and will not lead to any logicalconclusions. Data should be comparable over time and over space.

THE NATURE OF A STATISTICAL STUDY

Having briefly looked info the definition of Statistics, we should know at this stage as towhat the nature of a Statistical study is. Whether a given problem pertains to business orto some other field, there are some well defined steps that need to be followed in orderto reach meaningful conclusions.

1. Formulation of the Problem: To begin with, we have to formulate a problem onwhich a study is to be done. We should understand the problem as clearly as possible.We should know its scope so that we do not go beyond it or exclude some relevantaspect.

2. Objectives of the Study: We should know what the objectives of the proposedstudy are. We should ensure that the objectives are not extremely ambitious or else thestudy may fail to achieve them because of limitations of time, finance or evencompetence of those conducting the study.

3. Determining Sources of Data: The problem and the objectives, thus properlyunderstood, will enable us to know as to what data are required to conduct the study.We have to decide whether we should collect primary data or depend exclusively onsecondary data. Sometimes the study is based on both the secondary and the primarydata. When study is to be based on secondary data, whether partly or fully, it isnecessary to ensure that the data are quite suitable and adequate for the objectives ofthe study.

4. Designing Data Collection Forms: Once the decision in favour of collection ofprimary data is taken, one has to decide the mode of their collection. The two methodsavailable are: (i) observational method, and (ii) survey method. Suitable questionnaire isto be designed to collect data from respondents in a field survey.

5. Conducting the Field Survey: Side by side when the data collection forms arebeing designed, one has to decide whether a census surveyor a sample survey is to beconducted. For the latter, a suitable sample design and the sample size are to be chosen.The field survey is then conducted by interviewing sample respondents. Sometimes, thesurvey is done by mailing questionnaires to the respondents instead of contacting thempersonally.

6. Organising the Data: The field survey provides raw data from the respondents. Itis now necessary to organise these data in the form of suitable tables and charts so thatwe may be aware of their salient features.

7. Analysing the Data: On the basis of the preliminary examination of the datacollected as well as the nature and scope of our problem, we have to analyse data. Asseveral statistical techniques are available, we should take special care to ensure that themost appropriate technique is selected for this purpose.

8. Reaching Statistical bindings: The analysis in the preceding step will bring outsome statistical findings of the study. Now we have to interpret these findings in termsof the concrete problem with which we started our investigation.

9. Presentation of Findings: Finally, we have to present the findings of the study,properly interpreted, in a suitable form. Here, the choice is between an oral presentationand a written one. In the case of an oral presentation, one has to be extremely selectivein choosing the material, as in a limited time one has to provide a broad idea of thestudy as well as its major findings to be understood by the audience in properperspective. In case of a written presentation, a report has to be prepared. It should bereasonably comprehensive and should have graphs and diagrams to facilitate the readerin understanding it in all its ramifications.

IMPORTANCE OF STATISTICS IN BUSINESS

There is an increasing realisation of the importance of Statistics in various quarters.This is reflected in the increasing use of Statistics in the government, industry, business,agriculture, mining, transport, education, medicine, and so on. As we are concernedwith the use of Statistics in business and industry here, the description given below isconfined to these areas only.

Three major functions where statistics can be found useful in a business enterprise:

A. The planning of operations - This may relate to either special projects or to therecurring activities of a firm over a specified period.

B. The setting up of standards - This may relate to the size of employment, volumeof sales, fixation of quality norms for the manufactured product, norms for the dailyoutput, and so forth.

C. The function of control - This involves comparison of actual production achievedagainst the norm or target set earlier. In case the production has fallen short of thetarget, it gives remedial measures so that such a deficiency does not occur again.

A point worth noting here is that although these three functions - planning ofoperations, setting standards, and control-are separate, but in practice they are verymuch interrelated.

Various authors have highlighted the importance of Statistics in business. For instance,Croxton and Cowden give numerous uses of Statistics in business such as projectplanning, budgetary planning and control, inventory planning and control, qualitycontrol, marketing, production and personnel administration. Within these also theyhave specified certain areas where Statistics is very relevant. Irwing W. Burr, dealingwith the place of Statistics in an industrial organisation, specifies a number of areaswhere Statistics is extremely useful. These are: customer wants and market research,development design and specification, purchasing, production, inspection, packagingand shipping, sales and complaints, inventory and maintenance, costs, managementcontrol, industrial engineering and research.

It can be seen that both the lists are extremely comprehensive. This clearly points outthat specific statistical problems arising in the course of business operations aremultitudinous. As such, one may do no more than highlight some of the more importantones to emphasise the relevance of Statistics to the business world.

Personnel Management

This is another sphere in business where statistical methods can be used. Here, one isconcerned with the fixation of wage rates, incentive norms and performance appraisal ofindividual employee. The concept of productivity is very relevant here. On the basis ofmeasurement of productivity, the productivity bonus is awarded to the workers.

Comparisons of wages and productivity are undertaken in order to ensure increases inindustrial productivity.

Seasonal Behaviour

A business firm engaged in the sale of certain product has to decide how much stock ofthat product should be kept. If the product is subject to seasonal fluctuations then itmust know the nature of seasonal fluctuations in demand. For this purpose, seasonalindex of consumption may be required. If the firm can obtain such data or construct aseasonal index on its own then it can keep a limited stock of the product in lean monthsand large stocks in the remaining months. In this way, it will avoid the blocking of fundsin maintaining large stocks in the lean months. It will also not miss any opportunity tosell the product in the busy season by maintaining adequate stock of the product duringsuch a period.

Export Marketing

Developing countries have started giving considerable importance to their exports.Here, too, quality is an important factor on which exports depend. This apart, theconcerned firm must know the probable countries where its product can be exported.Before that, it must select the right product, which has considerable demand in theoverseas markets. This is possible by carefully analysing the statistics of imports andexports. It may also be necessary to undertake a detailed survey of overseas markets toknow more precisely the export potential of a given product.

Maintenance of Cost Records

Cost is an important consideration for a business enterprise. It has to ensure that cost ofproduction, which includes cost of raw materials, wages, and so forth, does not mountup or else this would jeopardize its competitiveness in the market. This implies that ithas to maintain proper cost records and undertake an analysis of cost data from time totime.

Management of Inventory

Closely related to the cost factor is the problem of inventory management. In order toensure that the production process continues uninterrupted, the business firm has tomaintain an adequate inventory. At the same time, excessive inventory means blockingof funds that could have been utilized elsewhere. Thus, the firm has to determine amagnitude of inventory that is neither excessive nor inadequate.

While doing so, it has to bear in mind the probable demand for its product. All theseaspects can be well looked after if proper statistics are maintained and analyzed.

Expenditure on Advertising and Sales

A number of times business firms are interested to know whether there is an associationbetween two or more variables such as advertising expenditure and sales. In view ofincreasing competitiveness, business and industry spend a large amount on advertising.It is in their interest to find out whether such advertising expenditure promotes thesales. Here, by using correlation and regression techniques it can be ascertained that theadvertising expenditure is worthwhile of not.

Mutual Funds

Mutual funds which have come into existence in recent years, provide an avenue to aperson to invest his savings so that he may get a reasonably good return. Differentmutual funds have different objectives as they have varying degrees of risk involved inthe companies they invest in. Here, Statistics provides certain tools or techniques to aconsultant or financial adviser through which he can provide sound advice to aprospective investor.

Relevance in Banking and Insurance Institutions

Banks and insurance companies frequently use varying statistical techniques in theirrespective areas of operation. They have to maintain their accounts and analyze these toexamine their performance over a specified period.

The above discussion is only illustrative and there are numerous other areas where theuse of Statistics is so common that without its use they may have to close down theiroperations.

STATISTICAL QUALITY CONTROL METHODS

In the sphere of production, for example, statistics can be useful in various ways toensure the production of quality goods. This is achieved by identifying and rejectingdefective or substandard goods. The sale targets can be fixed on the basis of saleforecasts, which are done by using varying methods of forecasting. Analysis of salesdone against the targets set earlier would indicate the deficiency in achievement, whichmay be on account of several causes: (i) targets were too high and unrealistic (ii)salesmen's performance has been poor (iii) emergence of increase in competition, and(iv) poor quality of company's product, and so on. These factors can be furtherinvestigated.

LIMITATIONS OF STATISTICS

The preceding discussion highlighting the importance of Statistics in business shouldnot lead anyone to conclude that Statistics is free from any limitation. As we shall seehere, Statistics has a number of limitations.

There are certain phenomena or concepts where Statistics cannot be used. This isbecause these phenomena or concepts are not amenable to measurement. For example,

beauty, intelligence, courage cannot be quantified. Statistics has no place in all suchcases where quantification is not possible.

1. Statistics reveal the average behaviour, the normal or the general trend. Anapplication of the 'average' concept if applied to an individual or a particular situationmay lead to a wrong conclusion and sometimes may be disastrous. For example, onemay be misguided when told that the average depth of a river from one bank to the otheris four feet, when there may be some points in between where its depth is far more thanfour feet. On this understanding, one may enter those points having greater depth,which may be hazardous.

2. Since Statistics are collected for a particular purpose, such data may not be relevantor useful in other situations or cases. For example, secondary data (i.e., data originallycollected by someone else) may not be useful for the other person.

3. Statistics is not 100 percent precise as is Mathematics or Accountancy. Those who useStatistics should be aware of this limitation.

4. In Statistical surveys, sampling is generally used as it is not physically possible tocover all the units or elements comprising the universe. The results may not beappropriate as far as the universe is concerned. Moreover, different surveys based onthe same size of sample but different sample units may yield different results.

5. At times, association or relationship between two or more variables is studied inStatistics, but such a relationship does not indicate 'cause and effect' relationship. Itsimply shows the similarity or dissimilarity in the movement of the two variables. Insuch cases, it is the user who has to interpret the results carefully, pointing out the typeof relationship obtained.

6. A major limitation of Statistics is that it does not reveal all pertaining to a certainphenomenon.

7. There is some background information that Statistics does not cover. Similarly, thereare some other aspects related to the problem on hand, which are also not covered. Theuser of Statistics has to be well informed and should interpret Statistics keeping in mindall other aspects having relevance on the given problem.

SUMMARY

This chapter outlined the importance and growth of statistics. Various applications ofstatistics in the domain of management have been dealt in detail.

KEY TERMS

· Statistics· Statistical quality control methods· Seasonal behaviour

IMPORTANT QUESTIONS

1. Define statistics

2. What do you mean by statistical quality methods?

3. Explain the application of statistics in various business domains.

- End of Chapter -

LESSON – 5

ESTIMATION OF POPULATION PARAMETERS

OBJECTIVE

· To acquire knowledge of estimation of parameter

STRUCTURE

· Estimation of population parameters· Measure of central tendency· Mean, median, mode· Geometric mean· Harmonic mean

A population is any entire collection of people, animals, plants or things from which wemay collect data. It is the entire group we are interested in, which we wish to describe ordraw conclusions about.

In order to make any generalizations about a population, a sample, that is meant to berepresentative of the population, is often studied. For each population there are manypossible samples. A sample statistic gives information about a corresponding populationparameter. For example, the sample mean for a set of data would give information aboutthe overall population mean.

It is important that the investigator carefully and completely defines the populationbefore collecting the sample, including a description of the members to be included.

Example

The population for a study of infant health might be all children born in the India, in the1980's. The sample might be all babies born on 7th May in any of the years.

Population Parameters

Parameter is a value, usually unknown (and which therefore has to be estimated), usedto represent a certain population characteristic. For example, the population mean is aparameter that is often used to indicate the average value of a quantity.

Within a population, a parameter is a fixed value which does not vary. Each sampledrawn from the population has its own value of any statistic that is used to estimate thisparameter. For example, the mean of the data in a sample is used to give informationabout the overall mean in the population from which that sample was drawn.

MEASURES OF CENTRAL LOCATION (OR CENTRAL TENDENCY)

The most important objective of statistical analysis is to determine a single value for theentire mass of data, which describes the overall level of the group of observations andcan be called a representative set of data. It tells us where the centre of the distributionof data is located on the scale that we are using. There are several such measures, but weshall discuss only those that are most commonly used. These are: Arithmetic Mean,Mode and Median. These values are very useful in not only presenting the overallpicture of the entire data, but also for the purpose of making comparisons among two ormore sets of data.

As an example, questions like, "How hot is the month of June in Mumbai?" can beanswered, generally, by a single figure of the average temperature for that month. Forthe purpose of comparison, suppose that we want to find out if boys and girls at the age10 differ in height. By taking the average height of boys of that age and the averageheight of the girls of the same age, we can compare and note the difference.

While, arithmetic mean is the most commonly used measure of central location, modeand median arc more suitable measures under certain set of conditions and for certaintypes of data. However, all measures of central tendency should meet the followingrequisites:

· It should be easy to calculate and understand.· It should be rigidly defined. It should have one and only one interpretation so

that the personal prejudice or bias of the investigator does not affect the value orits usefulness.

· It should be representative of the data. If it is calculated from a sample, then thesample should be random enough to be accurately representing the population.

· It should have sampling stability. It should not be affected by samplingfluctuations. This means that if we pick 10 different groups of college students atrandom and we compute the average of each group, then we should expect to getapproximately the same value from these groups.

· It should not be affected much by extreme values. If a few very small or very largeitems are presented in the data, they will unduly influence the value of theaverage by shifting it to one side or the other and hence the average would not be

really typical of the entire series. Hence, the average chosen should be such that itis not unduly influenced by extreme values.

Let us consider these three measures of the central tendency:

MODE

In statistics, mode means the most frequent value assumed by a random variable, oroccurring in a sampling of a random variable. The term is applied both to probabilitydistributions and to collections of experimental data.

Like the statistical mean and the median, die mode is a way of capturing importantinformation about a random variable or a population in a single quantity. The mode is ingeneral different from mean and median, and may be very different for strongly skeweddistributions.

The mode is not necessarily unique, since the same maximum frequency may beattained at different values. The worst case is given by so-called uniform distributions,in which all values are equally likely.

Mode of a probability distribution

The mode of a probability distribution is the value at which its probability densityfunction attains its maximum value, so, informally speaking; the mode is at the peak.

Mode of a sample

The mode of a data sample is the element that occurs most often in the collection. Forexample, the mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6. Given the list ofdata [1, 1, 2, 4, 4] the mode is not unique.

For a sample from a continuous distribution, such as [0.935..., 1.211..., 2.430..., 3.668...,3.874...], the concept is unusable in its raw form, since each value will occur preciselyonce. The usual practice is to discreteise the data by assigning the values to equidistantintervals, as for making a histogram, effectively replacing the values by the midpoints ofthe intervals they are assigned to. The mode is then the value where the histogramreaches its peak. For small or middle-sized samples the outcome of this procedure issensitive to the choice of interval width if chosen too narrow or too wide; typically oneshould have a sizable fraction of the data concentrated in a relatively small number ofintervals (5 to 10), while the fraction of the data falling outside these intervals is alsosizable.

Comparison of mean, median and mode

For a probability distribution, the mean is also called the expected value of the randomvariable. For a data sample, the mean is also called the average.

When do these measures make sense?

Unlike mean and median, the concept of mode also makes sense for "nominal data" (i.e.,not consisting of numerical values). For example, taking a sample of Korean familynames, one might find that "Kim" occurs more often than any other name. Then "Kim"might be called the mode of the sample. However, this use is not common.

Unlike median, the concept of mean makes sense for any random variable assumingvalues from a vector space, including the real numbers (a one-dimensional vector space)and the integers (which can be considered embedded in the real numbers). For example,a distribution of points in the plane will typically have a mean and a mode, but theconcept of median does not apply. The median makes sense when there is a linear orderon the possible values.

Uniqueness and Definedness

For the remainder, the assumption is that we have (a sample of) a real-valued randomvariable.

For some probability distributions, the expected value may be infinite or undefined, butif defined, it is unique. The average of a (finite) sample is always defined. The median isthe value such that the fractions not exceeding it and not falling below it are both at least1/2. It is not necessarily unique, but never infinite or totally undefined. For a datasample it is the "halfway" value when the list of values is ordered in increasing value,where usually for a list of even length the numerical average is taken of the two valuesclosest to "halfway". Finally, as said before, the mode is not necessarily unique.Furthermore, like the mean, the mode of a probability distribution can be (plus orminus)-infinity, but unlike the mean it cannot be just undefined. For a finite datasample, the mode is one (or more) of the values in the sample and is itself then finite.

Properties

Assuming definedness, and for simplicity uniqueness, the following are some of themost interesting properties.

All three measures have the following property: If the random variable (or each valuefrom the sample) is subjected to the linear or affine transformation which replaces Xbyax+b, so are the mean, median and mode.

However, if there is an arbitrary monotonic transformation, only the median follows; forexample, if X is replaced by exp(X), the median changes from m to exp(m) but the meanand mode won't.

Except for extremely small samples, the median is totally insensitive to "outliers" (suchas occasional, rare, false experimental readings). The mode is also very robust in thepresence of outliers, while the mean is rather sensitive.

In continuous uni-modal distributions the median lies, as a rule of thumb, between themean and the mode, about one third of the way going from mean to mode. In a formula,median = (2 x mean + mode)/3. This rule, due to Karl Pearson, is however not a hardand fast rule. It applies to distributions that resemble a normal distribution.

Example for a skewed distribution

A well-known example of a skewed distribution is personal wealth: Few people are veryrich, but among those some are excessively rich. However, many are rather poor.

A well-known class of distributions that can be arbitrarily skewed is given by the log-normal distribution. It is obtained by transforming a random variable X having anormal distribution into random variable Y = exp(X). Then the logarithm of randomvariable Y is normally distributed, whence the name.

Taking the mean μ of X to be 0, the median of Y will be 1, independent of the standarddeviation σ of X. This is so because X has a symmetric distribution, so its median is also0. The transformation from X to Y is monotonic, and so we find the median exp(0) = 1for Y.

When X has standard deviation σ = 0.2, the distribution of Y is not very skewed. We find(see under Log-normal distribution), with values rounded to four digits:

Mean = 1.0202

Mode = 0.9608

Indeed, the median is about one third on the way from mean to mode.

When X has a much larger standard deviation, σ = 5, the distribution of Y is stronglyskewed. Now

Mean = 7.3891

Mode = 0.0183

Here, Pearson's rule of thumb fails miserably.

MEDIAN

In probability theory and statistics, a median is a number dividing the higher half of asample, a population, or a probability distribution from the lower half. The median of afinite list of numbers can be found by arranging all the observations from lowest value tohighest value and picking the middle one. If there is an even number of observations,one often takes the mean of the two middle values.

At most, half the population has values less than the median and at most half havevalues greater than the median. If both groups contain less than half the population,then some of the population is exactly equal to the median.

Popular explanation

The difference between the median and mean is illustrated in a simple example.Suppose 19 paupers and one billionaire are in a room. Everyone removes all money fromtheir pockets and puts it on a table. Each pauper puts $5 on the table; the billionaireputs $1 billion (that is, $109) there. The total is then $1,000,000,095. If that money isdivided equally among the 20 persons, each gets $50,000,004.75. That amount is themean (or "average") amount of money that the 20 persons brought into the room. Butthe median amount is $5, since one may divide the group into two groups of 10 personseach, and say that everyone in the first group brought in no more than $5, and eachperson in the second group brought in no less than $5. In a sense, the median is theamount that the typical person brought in. By contrast, the mean (or "average") is not atall typical, since no one present - pauper or billionaire - brought in an amountapproximating $50,000,004.75.

Non-uniqueness

There may be more than one median. For example if there are an even number of cases,and the two middle values are different, then there is no unique middle value. Notice,however, that at least half the numbers in the list are less than or equal to either of thetwo middle values, and at least half are greater than or equal to either of the two values,and the same is true of any number between the two middle values. Thus either of thetwo middle values and all numbers between them are medians in that case.

Measures of statistical dispersion

When the median is used as a location parameter in descriptive statistics, there areseveral choices for a measure of variability: the range, the inter-quartile range, and theabsolute deviation. Since the median is the same as the second quartile, its calculation isillustrated in the article on quartiles. To obtain the median of an even number ofnumbers, find the average of the two middle terms.

Medians of particular distributions

The median of a normal distribution with mean μ and variance σ2 is μ. In fact, for anormal distribution, mean = median = mode.

The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also themean.

Medians in descriptive statistics

The median is primarily used for skewed distributions, which it represents differentlythan the arithmetic mean. Consider the multiset {1, 2, 2, 2, 3, 9}. The median is 2 in thiscase, as is the mode, and it might be seen as a better indication of central tendency thanthe arithmetic mean of 3.166....

Calculation of medians is a popular technique in summary statistics and summarizingstatistical data, since it is simple to understand and easy to calculate, while also giving ameasure that is more robust in the presence of outlier values than is the mean.

MEAN

In statistics, mean has two related meanings:

- The average in ordinary English, which is also called the arithmetic mean (and isdistinguished from the geometric mean or harmonic mean). The average is also calledsample mean. The expected value of a random variable, which is also called thepopulation mean.

- In statistics, ‘means’ are often used in geometry and analysis. A wide range of meanshave been developed for these purposes, which are not much used in statistics. See theother means section below for a list of means.

Sample mean is often used as an estimator of the central tendency such as thepopulation mean. However, other estimators are also used.

For a real-valued random variable X, the mean is the expectation of X. If the expectationdoes not exist, then the random variable has no mean.

For a data set, the mean is just the sum of all the observations divided by the number ofobservations. Once we have chosen this method of describing the communality of a dataset, we usually use the standard deviation to describe how the observations differ. Thestandard deviation is the square root of the average of squared deviations from themean.

The mean is the unique value about which the sum of squared deviations is a minimum.If you calculate the sum of squared deviations from any other measure of centraltendency, it will be larger than for the mean. This explains why the standard deviationand the mean are usually cited together in statistical reports.

An alternative measure of dispersion is the mean deviation, equivalent to the averageabsolute deviation from the mean. It is less sensitive to outliers, but less tractable whencombining data sets

Arithmetic Mean

The arithmetic mean is the "standard" average, often simply called the "mean".

The mean may often be confused with the median or mode. The mean is the arithmeticaverage of a set of values, or distribution; however, for skewed distributions, the mean isnot necessarily the same as the middle value (median), or most likely (mode). Forexample, mean income is skewed upwards by a small number of people with very largeincomes, so that the majority has an income lower than the mean. By contrast, themedian income is the level at which half the population is below and half is above. Themode income is the most likely income, and favors the larger number of people withlower incomes. The median or mode is often more intuitive measures of such data.

That said, many skewed distributions are best described by their mean - such as theExponential and Poisson distributions.

An amusing example…

Most people have an above average number of legs. The mean number of legs is going tobe less than 2, because there are people with one leg, people with no legs and no peoplewith more than two legs. So since most people have two legs, they have an above averagenumber.

Geometric Mean

The geometric mean is an average that is useful for sets of numbers that are interpretedaccording to their product and not their sum (as is the case with the arithmetic mean).For example rates of growth.

For example, the geometric mean of 34, 27, 45, 55, 22, 34 (six values) is (34 x 27 x 45 x55 x 22 x 34)1/6 = (1699493400)1/6 = 34.545

Harmonic Mean

The harmonic mean is an average which is useful for sets of numbers which are definedin relation to some unit, for example speed (distance per unit of time).

An example…

An experiment yields the following data: 34, 27, 45, 55, 22, 34. We need to find theharmonic mean. No. of items is 6, therefore n = 6. Value of the denominator in theformula is 0.181719152307. Reciprocal of this value is 5.50299727522. Now, we multiplythis by ‘n’ to get the harmonic mean as 33.0179836513.

Weighted Arithmetic Mean

The weighted arithmetic mean is used, if one wants to combine average values .romsamples of the same population with different sample sizes:

The weights ωi represent the bounds of the partial sample. In other applications theyrepresent a measure for the reliability of the influence upon the mean by respectivevalues.

SUMMARY

This chapter has given the meaning of population parameters. The procedures ofmeasuring the above population parameters are dealt with in detail in the chapter.

KEYTERMS

· Population parameters· Mean, Mode and Median· Arithmetic mean· Geometric mean· Harmonic mean· Skewed distribution

IMPORTANT QUESTIONS

1. Explain the methods to measure the Median, Mode and Mean

2. What are the different types of Means?

- End of Chapter -

LESSON – 6

HYPOTHESIS TESTING

OBJECTIVES

· To learn the process of Hypothesis Testing· To find out the details of Null hypothesis and Alternate hypothesis· To learn the precise meaning of probability value· To understand the Type I error and Type II errors· To gain knowledge on various methods to test hypothesis

STRUCTURE

· Hypothesis test· Statistical and practical significance· One and two failed tests· Type I and Type II Errors

Statistical hypothesis is an assumption about a population parameter. Thisassumption may or may not be true.

The best way to determine whether a statistical hypothesis is true is to examine theentire population. Since this is often impractical, researchers typically examine arandom sample from the population. If the sample data are consistent with thestatistical hypothesis, the hypothesis is accepted if not, the hypothesis is rejected.

There are two types of statistical hypotheses.

· Null hypothesis: usually the hypothesis that sample observations result purelyfrom chance effects.

· Alternative hypothesis: the hypothesis that sample observations are influenced bysome non-random cause.

For example, suppose we wanted to determine whether a coin was fair and balanced. Anull hypothesis might be that half the flips would result in Heads and half in Tails. Thealternative hypothesis might be that the number of Heads and Tails would be very

different. Suppose we flipped the coin 50 times resulting in 40 Heads and 10 Tails Giventhis result, we would be inclined to reject the null hypothesis and accept the alternativehypothesis.

HYPOTHESIS TESTS

Statisticians follow a formal process to determine whether to accept or reject a nullhypothesis, based on sample data. This process, called hypothesis testing, consists offour steps.

1. Formulate the hypotheses. This involves stating the null and alternativehypotheses. The hypotheses are stated in such a way that they are mutually exclusive.That is, if one is true, the other must be false, and vice versa.

2. Identify the test statistic. This involves specifying the statistic (e.g., a mean score,proportion) that will be used to assess the validity of the null hypothesis.

3. Formulate a decision rule. A decision rule is a procedure that the researcher usesto decide whether to accept or reject the null hypothesis.

4. Accept or reject the null hypothesis. Use the decision rule to evaluate the teststatistic. If the statistic is consistent with the null hypothesis, accept the null hypothesis;otherwise, reject the null hypothesis.

This section provides an introduction to hypothesis testing. Basic analysis involves somehypothesis testing. Examples of hypotheses generated in marketing research abound

· The department store is being patronized by more than 10 percent of thehouseholds

· The heavy and light users of a brand differ in terms of psychographiccharacteristics

· One hotel has a more upscale image than its close competitor· Familiarity with a restaurant results in greater preference for that restaurant.

The null hypothesis is a hypothesis about a population parameter. The purpose ofhypothesis testing is to test the viability of the null hypothesis in the light ofexperimental data. Depending on the data, the null hypothesis either will or will not berejected as a viable possibility.

Consider a researcher interested in whether the time to respond to a tone is affected bythe consumption of alcohol. The null hypothesis is that μ1 - μ2 = 0, where μ1 is the meantime to respond after consuming alcohol and μ2 is the mean time to respond otherwise.Thus, the null hypothesis concerns the parameter μ1 - μ2 and the null hypothesis is thatthe parameter equals zero.

The null hypothesis is often the reverse of what the experimenter actually believes; it isput forward to allow the data to contradict it. In the experiment on the effect of alcohol,

the experimenter probably expects alcohol to have a harmful effect. If the experimentaldata show a sufficiently large effect of alcohol, then the null hypothesis that alcohol hasno effect can be rejected.

It should be stressed that researchers very frequently put forward a null hypothesis inthe hope that they can discredit it. For a second example, consider an educationalresearcher who designed a new way to teach a particular concept in science, and wantedto test experimentally whether this new method worked better than the existing method.The researcher would design an experiment comparing the two methods. Since the nullhypothesis would be that there is no difference between the two methods, the researcherwould be hoping to reject the null hypothesis and conclude that the method he or shedeveloped is the better of the two.

The symbol H0 is used to indicate the null hypothesis. For the example just given, thenull hypothesis would be designated by the following symbols: H0: μ1 - μ2 = 0, or byH0: μ1 = μ2

The null hypothesis is typically a hypothesis of no difference as in this example where itis the hypothesis of no difference between population means. That is why the word"null" in "null hypothesis" is used - it is the hypothesis of no difference.

Despite the "null" in "null hypothesis", there are occasions when the parameter is nothypothesized to be 0. For instance, it is possible for the null hypothesis to be that thedifference between population means is a particular value. Or, the null hypothesis couldbe that the mean SAT score in some population is 600. The null hypothesis would thenbe stated as: H0: μ = 600. Although the null hypotheses discussed so far have allinvolved the testing of hypotheses about one or more population means, null hypothesescan involve any parameter.

An experiment investigating the correlation between job satisfaction and performanceon the job would test the null hypothesis that the population correlation (ρ) is 0.

Symbolically, H0: ρ = 0. Some possible null hypotheses are given below:

H0: μ = 0

H0: μ = 10

H0: μ1 - μ2 = 0

H0: π = 0.5

H0: π1- π2 = 0

H0: μ1 - μ2 - μ3

H0: ρ1 – ρ2 = 0

Steps in hypothesis testing

1. The first step in hypothesis testing is to specify the null hypothesis (H0) and thealternative hypothesis (H1). If the research concerns whether one method of presentingpictorial stimuli leads to better recognition than another, the null hypothesis wouldmost likely be that there is no difference between methods (H0: μ1 - μ2 = 0). Thealternative hypothesis would be H1: μ1 ≠ μ2. If the research concerned the correlationbetween grades and SAT scores, the null hypothesis would most likely be that there is nocorrelation (H0: ρ = 0). The alternative hypothesis would be H0: ρ ≠ 0.

2. The next step is to select a significance level. Typically the 0.05 or the 0.01 level isused.

3. The third step is to calculate a statistic analogous to the parameter specified by thenull hypothesis. If the null hypothesis were defined by the parameter μ1 - μ2, then thestatistic M1 - M2 would be computed.

4. The fourth step is to calculate the probability value (often called the p-value). The pvalue is the probability of obtaining a statistic as different or more different from theparameter specified in the null hypothesis as the statistic computed from the data. Thecalculations are made assuming that the null hypothesis is true.

5. The probability value computed in Step 4 is compared with the significance levelchosen in Step 2. If the probability is less than or equal to the significance level, then thenull hypothesis is rejected; if the probability is greater than the significance level thenthe null hypothesis is not rejected. When the null hypothesis is rejected, the outcome issaid to be “statistically significant”; when the null hypothesis is not rejected then theoutcome is said be “not statistically significant”.

6. If the outcome is statistically significant, then the null hypothesis is rejected in favorof the alternative hypothesis. If the rejected null hypothesis were that μ1 - μ2 = 0, thenthe alternative hypothesis would be that μ1 ≠ μ2. If M1 were greater than M2 then theresearcher would naturally conclude that μ1 ≥ μ2.

7. The final step is to describe the result and the statistical conclusion in anunderstandable way. Be sure to present the descriptive statistics as well as whether theeffect was significant or not. For example, a significant difference between a group thatreceived a drug and a control group might be described as follows:

Subjects in the drug group scored significantly higher (M = 23) than did subjects in thecontrol group (M = 17), t(18) = 2.4, p = 0.027. The statement that "t(18) = 2.4" has to dowith how the probability value (p) was calculated. A small minority of researchers mightobject to two aspects of this wording. First, some believe that the significance levelrather than the probability level should be reported. The argument for reporting theprobability value is presented in another section. Second, since the alternativehypothesis was stated as μ1 ≠ μ2, some might argue that it can only be concluded that thepopulation means differ and not that the population mean.

This argument is misguided. Intuitively, there are strong reasons for inferring that thedirection of the difference in the population is the same as the difference in the sample.There is also a more formal argument. A non significant effect might be described asfollows:

Although subjects in the drug group scored higher (M = 23) than did subjects in thecontrol group (M = 20), the difference between means was not significant, t(18) = 1.4. p= 0.179. It would not have been correct to say that there was no difference between theperformances of the two groups. There was a difference. It is just that the difference wasnot large enough to rule out chance as an explanation of the difference. It would alsohave been incorrect to imply that there is no difference in the population. Be sure not toaccept the null hypothesis.

The Precise Meaning of the Probability Value

There is often confusion about the precise meaning of the probability computed in asignificance test. As stated in Step 4 of the steps in hypothesis testing, the nullhypothesis (H0) is assumed to be true. The difference between the statistic computed inthe sample and the parameter specified by H0 is computed and the probability ofobtaining a difference this large or large is calculated. This probability value is theprobability of obtaining data as extreme or more extreme than the current data(assuming H0 is true). It is not the probability of the null hypothesis itself. Thus, if theprobability value is 0.005, this does not mean that the probability that the nullhypothesis is true is .005. It means that the probability of obtaining data as different ormore different from the null hypothesis as those obtained in the experiment is 0.005.

The inferential step to conclude that the null hypothesis is false goes, as follows:

The data (or data more extreme) are very unlikely given that the null hypothesis is true.This means that: (1) a very unlikely event occurred or (2) the null hypothesis is false.The inference usually made is that the null hypothesis is false.

To illustrate that the probability is not the probability of the hypothesis, consider a testof a person who claims to be able to predict whether a coin will come up heads or tails.One should take a rather skeptical attitude toward this claim and require strongevidence to believe in its validity. The null hypothesis is that the person can predictcorrectly half the time (H0: π = 0.5). In the test, a coin is flipped 20 times and the personis correct 11 times. If the person has no special ability (H0 is true), then the probability ofbeing correct 11 or more times out of 20 is 0.41. Would someone who was originallyskeptical now believe that there is only a 0.41 chance that the null hypothesis is true?They almost certainly would not since they probably originally thought H0 had a veryhigh probability of being true (perhaps as high as 0.9999). There is no logical reason forthem to decrease their belief in the validity of the null hypothesis since the outcome wasperfectly consistent with the null hypothesis.

The proper interpretation of the test is as follows:

A person made a rather extraordinary claim and should be able to provide strongevidence in support of the claim if the claim is to be believed. The test provided dataconsistent with the null hypothesis that the person has no special ability since a personwith no special ability would be able to predict as well or better more than 40% of thetime. Therefore, there is no compelling reason to believe the extraordinary claim.However, the test does not prove the person cannot predict better than chance; it simplyfails to provide evidence that he or she can. The probability that the null hypothesis istrue is not determined by the statistical analysis conducted as part of hypothesis testing.Rather, the probability computed is the probability of obtaining data as different ormore different from the null hypothesis (given that the null hypothesis is true) as thedata actually obtained.

According to one view of hypothesis testing, the significance level should be specifiedbefore any statistical calculations are performed. Then, when the probability (p) iscomputed from a significance test, it is compared with the significance level. The nullhypothesis is rejected if p is at or below the significance level; it is not rejected if p isabove the significance level. The degree to which p ends up being above or below thesignificance level does not matter. The null hypothesis either is or is not rejected at thepreviously stated significance level. Thus, if an experimenter originally stated that he orshe was using the 0.05 significance level and p was subsequently calculated to be 0.042,then the person would reject the null hypothesis at the 0.05 level. If p had been 0.0001instead of 0.042 then the null hypothesis would still be rejected at the 0.05 level. Theexperimenter would not have any basis to be more confident that the null hypothesiswas false with a p of 0.0001 than with a p of 0.041. Similarly, if the p had been 0.051then the experimenter would fail to reject the null hypothesis.

He or she would have no more basis to doubt the validity of the null hypothesis than if phad been 0.482. The conclusion would be that the null hypothesis could not be rejectedat the 0.05 level. In short, this approach is to specify the significance level in advanceand use p only to determine whether or not the null hypothesis can be rejected at thestated significance level.

Many statisticians and researchers find this approach to hypothesis testing not only toorigid, but basically illogical. Who in their right mind would not have more confidencethat the null hypothesis is false with a p of 0.0001 than with a p of 0.042? The less likelythe obtained results (or more extreme results) under the null hypothesis, the moreconfident one should be that the null hypothesis is false. The null hypothesis should notbe rejected once and for all. The possibility that it was falsely rejected is always present,and, all else being equal, the lower the p value, the lower this possibility.

Statistical and Practical Significance

It is important not to confuse the confidence with which the null hypothesis can berejected with size of the effect. To make this point concrete, consider a researcherassigned the task of determining whether the video display used by travel agents forbooking airline reservations should be in color or in black and white. Market researchhad shown that travel agencies were primarily concerned with the speed with which

reservations can be made. Therefore, the question was whether color displays allowtravel agents to book reservations faster. Market research had also shown that in orderto justify the higher price of color displays, they must be faster by an average of at least10 seconds per transaction. Fifty subjects were tested with color displays and 50 subjectswere tested with black and white displays.

Subjects were slightly faster at making reservations on a color display (M = 504.7seconds) than on a black and white display (M = 508.2) seconds, although the differenceis small, it was statistically significant at the .05 significance level. Box plots of the dataare shown below.

The 95% confidence interval on the difference between means is:

-7.0 < μ colour – μ black & white ≤ -0.1

which means that the experimenter can be confident that the color display is between7.0 seconds and 0.1 seconds faster. Clearly, the difference is not big enough to justify themore expensive color displays. Even the upper limit of the 95% confidence interval(seven seconds) is below the minimum needed to justify the cost (10 seconds).Therefore, the experimenter could feel confident in his or her recommendation that theblack and white displays should be used. The fact that the color displays weresignificantly faster does not mean that they were much fasten It just means that theexperimenter can reject the null hypothesis that there is no difference between thedisplays.

The experimenter presented this conclusion to management but management did notaccept it. The color displays were so dazzling that despite the statistical analysis, theycould not believe that color did not improve performance by at least 10 seconds. Theexperimenter decided to do the experiment again, this time using 100 subjects for eachtype of display. The results of the second experiment were very similar to the first.Subjects were slightly faster at making reservations on a color display (M = 504.7seconds) than on a black and white display (M = 508.1 seconds). This time thedifference was significant at the 0.01 level rather than the 0.05 level found in the firstexperiment. Despite the fact that the size of the difference between means was no larger,

the difference was "more significant" due to the larger sample size used. If thepopulation difference is zero, then a sample difference of 3.4 or larger with a sample sizeof 100 is less likely than a sample difference of 3.5 or larger with a sample size of 50.

The 95% confidence interval on the difference between means is:

-5.8 < μ colour – μ black & white ≤ -0.9

and the 99% interval is:

-6.6 < μ colour – μ black & white ≤ -0.1

Therefore, despite the finding of a "more significant" difference between means theexperimenter can be even more certain that the color displays are only slightly betterthan the black and white displays. The second experiment shows conclusively that thedifference is less than 10 seconds.

This example was used to illustrate the following points:

(1) an effect that is statistically significant is not necessarily large enough to be ofpractical significance and

(2) the smaller of two effects can be "more significant" than the larger.

Be careful how you interpret findings reported in the media. If you read that a particulardiet lowered cholesterol significantly, this does not necessarily mean that the dietlowered cholesterol enough to be of any health value. It means that the effect oncholesterol in the population is greater than zero.

TYPE I AND II ERRORS

There are two kinds of errors that can be made in significance testing:

(1) a true null hypothesis can be incorrectly rejected and

(2) a false null hypothesis can fail to be rejected.

The former error is called a Type I error and the latter error is called a Type II error.These two types of errors are defined in the table.

The probability of a Type I error is designated by the Greek letter alpha (α) and is calledthe Type I error rate; the probability of a Type II error is designated by the Greekletter beta (β), and is called the Type II error rate.

A Type II error is only an error in the sense that an opportunity to reject the nullhypothesis correctly was lost. It is not an error in the sense that an incorrect conclusionwas drawn since no conclusion is drawn when the null hypothesis is not rejected. A TypeI error, on the other hand, is an error in every sense of the word. A conclusion is drawnthat the null hypothesis is false when, in fact, it is true. Therefore, Type I errors aregenerally considered more serious than Type II errors. The probability of a Type I error(α) is called the significance level and is set by the experimenter. There is a tradeoffbetween Type I and Type II errors. The more an experimenter protects himself orherself against Type I errors by choosing a low level, the greater the chance of a Type IIerror. Requiring very strong evidence to reject the null hypothesis makes it very unlikelythat a true null hypothesis will be rejected. However, it increases the chance that a falsenull hypothesis will not be rejected, thus lowering power. The Type I error rate is almostalways set at .05 or at .01, the latter being more conservative since it requires strongerevidence to reject the null hypothesis at the .01 level then at the .05 level.

One and Two Tailed Tests

In the section on "Steps in hypothesis testing", the fourth step involves calculating theprobability that a statistic would differ as much or more from parameter specified in thenull hypothesis as does the statistic obtained in the experiment. This statement impliesthat a difference in either direction would be counted. That is, if the null hypothesiswere H0: μ1 - μ2 = 0, and the value of the statistic M1 - M2 were +5, then the probabilityof M1 - M2 differing from zero by five or more (in either direction) would be computed.In other words, probability value would be the probability that either M1 - M2 ≥ 5 or M1 -M2 ≤ -5.Assume that the figure shown below is the sampling distribution of M1 - M2.

The figure shows that the probability of a value of +5 or more is 0.036 and that theprobability of a value of -5 or less is .036. Therefore the probability of a value eithergreater than or equal to +5 or less than or equal to -5 is 0.036 + 0.036 = 0.072.

A probability computed considering differences in both directions is called a "two-tailed" probability. The name makes sense since both tails of the sampling distributionare considered. There are situations in which an experimenter is concerned only withdifferences in one direction. For example, an experimenter may be concerned withwhether or not μ1 - μ2 is greater than zero. However, if μ1 - μ2 is not greater than zero,the experimenter may not care whether it equals zero or is less than zero. For instance, ifa new drug treatment is developed, the main issue is whether or not it is better than aplacebo. If the treatment is not better than a placebo, then it will not be used. It does notreally matter whether or not it is worse than the placebo.

When only one direction is of concern to an experimenter, then a "one-tailed" test canbe performed. If an experimenter were only to be concerned with whether or not μ1 - μ2

is greater than zero, then the one-tailed test would involve calculating the probability ofobtaining a statistic as greater than the one obtained in the experiment.

In the example, the one-tailed probability would be the probability of obtaining a valueof M1 - M2 greater than or equal to five given that the difference between populationmeans is zero.

The shaded area in the figure is greater than five. The figure shows that the one-tailedprobability is 0.036.

It is easier to reject the null hypothesis with a one-tailed than with a two-tailed test aslong as the effect is in the specified direction. Therefore, one-tailed tests have lowerType II error rates and more power than do two-tailed tests. In this example, the one-tailed probability (0.036) is below the conventional significance level of 0.05 whereasthe two-tailed probability (0.072) is not. Probability values for one-tailed tests are onehalf the value for two-tailed tests as long as the effect is in the specified direction.

One-tailed and two-tailed tests have the same Type I error rate. One-tailed tests aresometimes used when the experimenter predicts the direction of the effect in advance.This use of one-tailed tests is questionable because the experimenter can only reject the

null hypothesis if the effect is in the predicted direction. If the effect is in the otherdirection, then the null hypothesis cannot be rejected no matter how strong the effect is.A skeptic might question whether the experimenter would really fail to reject the nullhypothesis if the effect were strong enough in the wrong direction. Frequently the mostinteresting aspect of an effect is that it runs counter to expectations. Therefore, anexperimenter who committed himself or herself to ignoring effects in one direction maybe forced to choose between ignoring a potentially important finding and using thetechniques of statistical inference dishonestly. One-tailed tests are not used frequently.Unless otherwise indicated, a test should be assumed to be two-tailed.

Confidence Intervals & Hypothesis Testing

There is an extremely close relationship between confidence intervals and hypothesistesting. When a 95% confidence interval is constructed, all values in the interval areconsidered plausible values for the parameter being estimated. Values outside theinterval are rejected as relatively implausible. If the value of the parameter specified bythe null hypothesis is contained in the 95% interval then the null hypothesis cannot berejected at the 0.05 level. If the value specified by the null hypothesis is not in theinterval then the null hypothesis can be rejected at the 0.05 level. If a 99% confidenceinterval is constructed, then values outside the interval are rejected at the 0.01 level.

Imagine a researcher wishing to test the null hypothesis that the mean time to respondto an auditory signal is the same as the mean time to respond to a visual signal. The nullhypothesis therefore is: μ visual – μ auditory = 0.

Ten subjects were tested in the visual condition and their scores (in milliseconds) were:355, 421, 299, 460, 600, 580, 474, 511, 550, and 586.

Ten subjects were tested in the auditory condition and their scores were: 275, 320, 278,360, 430, 520, 464, 311, 529, and 326.

The 95% confidence interval on the difference between means is: 9 ≤ μ visual – μauditory ≤ 196.

Therefore only values in the interval between 9 and 196 are retained as plausible valuesfor the difference between population means. Since zero, the value specified by the nullhypothesis, is not in the interval, the null hypothesis of no difference between auditoryand visual presentation can be rejected at the 0.05 level. The probability value for thisexample is 0.034. Any time the parameter specified by a null hypothesis is not containedin the 95% confidence interval estimating that parameter, the null hypothesis can berejected at the 0.05 level or less. Similarly, if the 99% interval does not contain theparameter then the null hypothesis can be rejected at the 0.01 level. The null hypothesisis not rejected if the parameter value specified by the null hypothesis is in the intervalsince the null hypothesis would still be plausible.

However, since the null hypothesis would be only one of an infinite number of values inthe confidence interval, accepting the null hypothesis is not justified. There are many

arguments against accepting the null hypothesis when it is not rejected. The nullhypothesis is usually a hypothesis of no difference. Thus null hypothesis such as:

μ1 - μ2 = 0

π1 - π2 = 0

in which the hypothesized value is zero are most common. When the hypothesized valueis zero then there is a simple relationship between hypothesis testing and confidenceintervals:

If the interval contains zero then the null hypothesis cannot be rejected at the statedlevel of confidence. If the interval does not contain zero then the null hypothesis can berejected.

This is just a special case of the general rule stating that the null hypothesis can berejected if the interval does not contain the hypothesized value of the parameter andcannot be rejected if the interval contains the hypothesized value. Since zero iscontained in the interval, the null hypothesis that μ1 - μ2 = 0 cannot be rejected at the0.05 level since zero is one of the plausible values of μ1 - μ2. The interval contains bothpositive and negative numbers and therefore μ1 may be either larger or smaller than μ2.None of the three possible relationships between μ1 and μ2:

μ1 - μ2 = 0,

μ1 - μ2 > 0, and

μ1 - μ2 < 0

can be ruled out. The data are very inconclusive. Whenever a significance test fails toreject the null hypothesis, the direction of the effect (if there is one) is unknown.

Now, consider the 95% confidence interval:

6 < μ1 - μ2 ≤ 15

Since zero is not in the interval, the null hypothesis that μ1 - μ2 = 0 can be rejected at the0.05 level. Moreover, since all the values in the interval are positive, the direction of theeffect can be inferred: μ1 > μ2.

Whenever a significance test rejects the null hypothesis that a parameter is zero, theconfidence interval on that parameter will not contain zero. Therefore either all thevalues in the interval will be positive or all the values in the interval will be negative. Ineither case, the direction of the effect is known.

Define the Decision Rule and the Region of Acceptance

The decision rule consists of two parts: (1) a test statistic and (2) a range of values, calledthe region of acceptance. The decision rule determines whether a null hypothesis isaccepted or rejected. If the test statistic falls within the region of acceptance, the nullhypothesis is accepted; otherwise, it is rejected.

We define the region of acceptance in such a way that the chance of making a Type Ierror is equal to the significance level. Here is how that is done:

♦ Given the significance level α, find the upper limit (UL) of the range of acceptance.There are three possibilities, depending on the form of the null hypothesis -

i. If the null hypothesis is μ < M: The upper limit of the region of acceptance will beequal to the value for which the cumulative probability of the sampling distribution isequal to one minus the significance level. That is, P(x < UL) = 1 - α.

ii. If the null hypothesis is μ = M: The upper limit of the region of acceptance willbe equal to the value for which the cumulative probability of the sampling distribution isequal to one minus the significance level divided by 2. That is, P(x < UL) = 1 - α/2.

iii. If the null hypothesis is μ > M: The upper limit of the region of acceptance isequal to plus infinity.

♦ In a similar way, we find the lower limit (LL) of the range of acceptance. Again, thereare three possibilities, depending on the form of the null hypothesis.

i. If the null hypothesis is μ < M: The lower limit of the region of acceptance isequal to minus infinity.

ii. If the null hypothesis is μ = M: The lower limit of the region of acceptance will beequal to the value for which the cumulative probability of the sampling distribution isequal to the significance level divided by 2. That is, P(x < LL) = α/2

iii. If the null hypothesis is μ > M: The lower limit of the region of acceptance willbe equal to the value for which the cumulative probability of the sampling distribution isequal to the significance level. That is, P(x < LL) = α

The region of acceptance is defined by the range between LL and UL.

Accept or Reject the Null Hypothesis

Once the region of acceptance is defined, the null hypothesis can be tested againstsample data. Simply compute the test statistic. In this case, the test statistic is thesample mean. If the sample mean falls within the region of acceptance, the nullhypothesis is accepted; if not, it is rejected.

Other Considerations

When one tests a hypothesis in the real world, other issues may come into play. Here aresome suggestions that may be helpful.

♦ You will need to make an assumption about the sampling distribution of the meanscore. If the sample is relatively large (i.e., greater than or equal to 30), you can assume,based on the central limit theorem, that the sampling distribution will be roughlynormal. On the other hand, if the sample size is small (less than 30) and if thepopulation random variable is approximately normally distributed (i.e., has a bell-shaped curve), you can transform the mean score into a t-score. The t-score will have at-distribution.

♦ Assume that the mean of the sampling distribution is equal to the test value Mspecified in the null hypothesis.

♦ In some situations, you may need to compute the standard deviation of the samplingdistribution sx. If the standard deviation of the population σ is known, then sx = σ xsqrt[(1/n) - (1/N)], where n is the sample size and N is the population size. On the otherhand, if the standard deviation of the population σ is unknown, then

sx = s x sqrt of [(1/n) - (1/N)], where s is the sample standard deviation.

Example 1

An inventor has developed a new, energy-efficient lawn mower engine. He claims thatthe engine will run continuously for 5 hours (300 minutes) on a single gallon of regulargasoline. Suppose a random sample of 50 engines is tested. The engines run for anaverage of 295 minutes, with a standard deviation of 20 minutes. Test the nullhypothesis that the mean run time is 300 minutes against the alternative hypothesisthat the mean run time is not 300 minutes. Use a 0.05 level of significance.

Solution

There are four steps in conducting a hypothesis test, as described in the previoussections. We work through those steps below:

1. Formulate hypotheses

The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: μ = 300 minutes

Alternative hypothesis: μ < > 300 minutes

Note that these hypotheses constitute a two-tailed test. The null hypothesis will berejected if the sample mean is too big or if it is too small.

2. Identify the test statistic

In this example, the test statistic is the mean run time of the 50 engines in the sample =295 minutes.

3. Define the decision rule

The decision rule consists of two parts: (1) a test statistic and (2) a range of values, calledthe region of acceptance. We already know that the test statistic is a sample mean equalto 295. All that remains is to describe the region of acceptance; that is, to define thelower limit and the upper limit of the region. Here is how that is done.

a. Specify the sampling distribution. Since the sample size is large (greater thanor equal to 30), we assume that the sampling distribution of the mean is normal,based on the central limit theorem.

b. Define the mean of the sampling distribution. We assume that the mean of thesampling distribution is equal to the mean value that appears in the nullhypothesis - 300 minutes.

c. Compute the standard deviation of the sampling distribution. Here thestandard deviation of the sampling distribution sx is:

sx = σ x sqrt[(1/n) - (1/N)]

sx = 20 x sqrt[1/50] = 2.83

where s is the sample standard deviation, n is the sample size, and N is thepopulation size. In this example, we assume that the population size N is verylarge, so that the value 1/N is about zero.

4. Find the lower limit of the region of acceptance

Given a two-tailed hypothesis, the lower limit (LL) will be equal to the value for whichthe cumulative probability of the sampling distribution is equal to the significance leveldivided by 2. That is, P(x < LL) = α/2 = 0.05/2 = 0.025. To find this lower limit, we usethe Normal Distribution table. From table, cumulative probability = 0.025, mean = 300,and standard deviation = 2.83. The calculation tells us that the lower limit is 294.45,given those inputs.

a. Find the upper limit of the region of acceptance. Given a two-tailed hypothesis,the upper limit (UL) will be equal to the value for which the cumulativeprobability of the sampling distribution is equal to one minus the significancelevel divided by 2. That is, P(x < UL) = 1 - α/2 = 1 - 0.025 = 0.975. To find thisupper limit, we use the Normal Distribution Table. From table, cumulativeprobability = 0.975, mean = 300, and standard deviation = 2.83. The calculationtells us that the upper limit is 305.55, given those inputs.

b. Thus, we have determined that the region of acceptance is defined by thevalues between 294.45 and 305.55.

5. Accept or reject the null hypothesis

The sample mean in this example was 295 minutes. This value falls within the region ofacceptance. Therefore, we cannot reject the null hypothesis that a new engine runs for300 minutes on a gallon of gasoline.

Example 2

Bon Air Elementary School has 300 students. The principal of the school thinks that theaverage IQ of students at Bon Air is at least 110. To prove her point, she administers anIQ test to 20 randomly selected students. Among the sampled students, the average IQis 108 with a standard deviation of 10. Based on these results, should the principalaccept or reject her original hypothesis? Assume a significance level of 0.01.

Solution

There are four steps in conducting a hypothesis test, as described in the previoussections. We work through those steps below:

1. Formulate hypotheses.

The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: μ > 110

Alternative hypothesis: μ < 110

Note that these hypotheses constitute a one-tailed test. The null hypothesis will berejected if the sample mean is too small.

2. Identify the test statistic.

In this example, the test statistic is the mean IQ score of the 20 students in the sample.Thus, the test statistic is the mean IQ score of 108.

3. Define the decision rule. The decision rule consists of two parts: (1) a test statisticand (2) a range of values, called the region of acceptance. We already know that the teststatistic is a sample mean equal to 108. All that remains is to describe the region ofacceptance; that is, to define the lower limit and the upper limit of the region. Here ishow that is done.

a. Specify the sampling distribution. Since the sample size is small (less than 30),we assume that the sampling distribution of the mean follows a t-distribution.

b. Define the mean of the sampling distribution. We assume that the mean of thesampling distribution is equal to the mean value that appears in the nullhypothesis - 110.

c. Find the lower limit of the region of acceptance. Given a one-tailed hypothesis,the lower limit (LL) will be equal to the value for which the cumulativeprobability of the sampling distribution is equal to the significance level. That is,P(x < LL) = α = 0.01.

To find this lower limit, we use the T-Distribution Table. From table, cumulativeprobability = 0.01, population mean = 110, standard deviation = 2.16, anddegrees of freedom = 20 - 1 = 19. The calculation tells us that the sample mean is104.51, given those inputs. This is the lower limit of our region of acceptance.

d. Find the upper limit of the region of acceptance. Since we have a one-tailedhypothesis in which the null hypothesis states that the IQ is greater than 110, anybig number is consistent with the null hypothesis. Therefore, the upper limit isplus infinity.

Thus, we have determined that the range of acceptance is defined by the values between104.51 and plus infinity.

4. Accept or reject the null hypothesis.

The sample mean in this example was an IQ score of 108. This value falls within theregion of acceptance. Therefore, we cannot reject the null hypothesis that the average IQscore of students at Bon Air Elementary is equal to 110.

Power of a Hypothesis Test

When we conduct a hypothesis test, we accept or reject the null hypothesis based onsample data. Because of the random nature of sample data, our decision can have fourpossible outcomes.

· We may accept the null hypothesis when it is true. Thus, the decision is correct.· We may reject the null hypothesis when it is true. This kind of incorrect decision

is called a Type I error.· We may reject the null hypothesis when it is false. Thus, the decision is correct.· We may accept the null hypothesis when it is false. This kind of incorrect decision

is called a Type II error.

The probability of committing a Type I error is called the significance level and isdenoted by α. The probability of committing a Type II error is called Beta and is denotedby β. The probability of not committing a Type II error is called the power of the test.

How to Compute the Power of a Test

When a researcher designs a study to test a hypothesis, he/she should compute thepower of the test (i.e., the likelihood of avoiding a Type II error). Here is how to do that:

1. Define the region of acceptance.

(The process for defining the region of acceptance is described in the previous threelessons. See, for example, Hypothesis Tests of Mean Score, Hypothesis Tests ofProportion (Large Sample), and Hypothesis Tests of Proportion (Small Sample).)

2. Specify the critical value.

The critical value is an alternative to the value specified in the null hypothesis. Thedifference between the critical value and the value from the null hypothesis is called theeffect size. That is, the effect size is equal to the critical value minus the value from thenull hypothesis.

3. Compute power. Assume that the true population parameter is equal to the criticalvalue, rather than the value specified in the null hypothesis. Based on that assumption,compute the probability that the sample estimate of the population parameter will falloutside the region of acceptance. That probability is the power of the test.

Example 1: Power of the Hypothesis Test of a Mean Score

Two inventors have developed a new, energy-efficient lawn mower engine. One inventorsays that the engine will run continuously for 5 hours (300 minutes) on a single gallonof regular gasoline. Suppose a random sample of 50 engines is tested. The engines runfor an average of 295 minutes, with a standard deviation of 20 minutes. The inventortests the null hypothesis that the mean run time is 300 minutes against the alternativehypothesis that the mean run time is not 300 minutes, using a 0.05 level of significance.

The other inventor says that the new engine will run continuously for only 290 minuteson a gallon of gasoline. Find the power of the test to reject the null hypothesis, if thesecond inventor is correct.

Solution

The steps required to compute power are presented below.

1. Define the region of acceptance.

Earlier, we showed that the region of acceptance for this problem consists of the valuesbetween 294.45 and 305.55.

2. Specify the critical value.

The null hypothesis tests the hypothesis that the run time of the engine is 300 minutes.We are interested in determining the probability that the hypothesis test will reject the

null hypothesis, if the true run time is actually 290 minutes. Therefore, the critical valueis 290. Another way to express the critical value is through effect size. The effect size isequal to the critical value minus the hypothesized value. Thus, effect size is equal to 290- 300 = -10

3. Compute power.

The power of the test is the probability of rejecting the null hypothesis, assuming thatthe true population mean is equal to the critical value. Since the region of acceptance is294.45 to 305.55, the null hypothesis will be rejected when the sampled run time is lessthan 294.45 or greater than 305.55.

Therefore, we need to compute the probability that the sampled run time will be lessthan 294.45 or greater than 305.55. To do this, we make the following assumptions:

· The sampling distribution of the mean is normally distributed. (Because thesample size is relative large, this assumption can be justified by the central limittheorem.)

· The mean of the sampling distribution is the critical value, 290.· The standard deviation of the sampling distribution is 2.83. The standard

deviation of the sampling distribution was computed in a previous lesson

Given these assumptions, we first assess the probability that the sample run time will beless than 294.45. This is easy to do, using the Normal Calculator. We enter the followingvalues into the calculator: value = 294.45; mean = 290, and standard deviation = 2.83.Given these inputs, we find that the cumulative probability is 0.94207551. This meansthe probability that the sample mean will be less than 294.45 is 0.942.

Next, we assess the probability that the sample mean is greater than 305.55. Again, weuse the Normal Calculator. We enter the following values into the calculator: value =305.55; mean = 290; and standard deviation = 2.83. Given these inputs, we find that theprobability that the sample mean is less than 305.55 (i.e., the cumulative probability) is0.99999998. Thus, the probability that the sample mean is greater than 305.55 is 1 -0.99999998 or 0.00000002.

The power of the test is the sum of these probabilities: 0.94207551 + 0.00000002 =0.94207553. This means that if the true average run time of the new engine were 290minutes, we would correctly reject the hypothesis that the run time was 300 minutes94.2 percent of the time. Hence, the probability of a Type II error would be very small.Specifically, it would be 1 minus 0.942 or 0.058.

IMPORTANT STATISTICAL DEFINITIONS OF HYPOTHESIS TESTING

Alpha - The significance level of a test of hypothesis that denotes the probability ofrejecting a null hypothesis when it is actually true; In other words, it is the probability ofcommitting a Type I error.

Alternative Hypothesis - A hypothesis that takes a value of a population parameterdifferent from that used in the null hypothesis

Beta - The probability of not rejecting a null hypothesis when it actually is false. Inother words, it is the probability of committing a Type II error.

Critical region - The set of values of the test statistic that will cause us to reject thenull hypothesis.

Critical Value - The first (or 'boundary') value in the critical region.

Decision rule - If the calculated test statistic falls within the critical region, the nullhypothesis H0 is rejected. In contrast, if the calculated test statistic does not fall withinthe critical region, the null hypothesis is not rejected.

F-distribution - A continuous distribution that has two parameters (df for thenumerator and df for the denominator). It is mainly used to test hypotheses concerningvariances.

F-ratio - In ANOV A, it is the ratio of between column variance to within columnvariance.

Hypothesis - An unproven proposition or supposition that tentatively explains aphenomenon.

Null hypothesis - A statement about a status quo about a population parameter that isbeing tested.

One-tailed test - A statistical hypothesis test in which the alternative hypothesis isspecified such that only one direction of the possible distribution of values is considered.

Power of hypothesis test - The probability of rejecting the null hypothesis when it isfalse.

Significance level - The value of α that gives the probability of rejecting the nullhypothesis when it is true. This gives rise to Type I error.

Test criteria - Criteria consisting of (i) specifying a level of significance ex, (ii)determining a test statistic, (iii) determining the critical region(s), and (iv) determiningthe critical value(s)

Test Statistic - The value of Z or t calculated for a sample statistic such as the samplemean or the sample proportion.

Two-tail test - A statistical hypothesis test in which the alternative hypothesis is statedin such a way that it includes both the higher and the lower values of a parameter thanthe value specified in the null hypothesis.

Type I error - An error caused by rejecting a null hypothesis that is true.

Type II error - An error caused by failing to reject a null hypothesis that is not true.

SUMMARY

This chapter had given clear picture about the process of Hypothesis Testing and to findout the details of Null hypothesis and Alternate hypothesis. This lesson also has giventhe significance and differences between Type I error and Type II error. The detailedstep-wise procedures were given to perform the hypothesis testing. This chapter alsogives details about the calculation of P value.

KEY TERMS

· Hypothesis testing· Null hypothesis· Alternative Hypothesis· Type I error· Type II error· Probability value· One & two tailed tests· Decision rule· Confidence interval and Statistical significance

IMPORTANT QUESTIONS

1. What do you mean by Hypothesis testing?

2. Define: Null hypothesis and Alternative Hypothesis.

3. Write down the steps to be performed for Hypothesis test

4. What are the differences between Type I and Type II error?

5. How will calculate the Probability value?

6. What do you understand by one and two tailed test?

7. Define Decision rule

8. What is the significance of understanding of confidence intervals?

- End of Chapter -

LESSON - 7

CHI-SQUARE TEST

OBJECTIVES

· To learn the significance of Statistical tests.· To find out the details of Chi-square test, F-test and t-test· To learn the detailed procedures for doing above mentioned tests· To understand the concept of Measures of association

STRUCTURE

Bivariate tabular analysis

Chi-square requirements

Computing chi-square

Measure of Association

INTRODUCTION

Chi square is a non-parametric test of statistical significance for bivariate tabularanalysis (also known as crossbreaks). Any appropriately performed test of statisticalsignificance lets you know the degree of confidence you can have in accepting orrejecting a hypothesis. Typically, the hypothesis tested with chi square is whether or nottwo different samples (of people, texts, whatever) are different enough in somecharacteristic or aspect of their behavior that we can generalize from our samples, thatthe populations from which our samples are drawn are also different in the behavior orcharacteristic.

A non-parametric test, like chi square, is a rough estimate of confidence; it acceptsweaker, less accurate data as input than parametric tests (like t-tests and analysis ofvariance, for example) and therefore has less status in the pantheon of statistical tests.Nonetheless, its limitations are also its- strengths; because chi square is more 'forgiving'in the data it will accept, it can be used in a wide variety of research contexts.

Chi square is used most frequently to test the statistical significance of results reportedin bivariate tables, and interpreting bivariate tables is integral to interpreting the resultsof a chi square test, so we'll take a look at bivariate tabular (crossbreak) analysis.

Bivariate Tabular Analysis

Bivariate tabular (crossbreak) analysis is used when you are trying to summarize theintersections of independent and dependent variables and understand the relationship(if any) between those variables. For example, if we wanted to know if there is anyrelationship between the biological sex of American undergraduates at a particularuniversity and their footwear preferences, we might select 50 males and 50 females asrandomly as possible, and ask them, "On average, do you prefer to wear sandals,sneakers, leather shoes, boots, or something else?" In this example, our independentvariable is biological sex (in experimental research, the independent variable is activelymanipulated by the researcher, for example, whether or not a rat gets a food pellet whenit pulls on a striped bar. In most sociological research, the independent variable is notactively manipulated in this way, but controlled by sampling for, e.g., males vs. females).Put another way, the independent variable is the quality or characteristic that youhypothesize helps to predict or explain some other quality or characteristic (thedependent variable). We control the independent variable (and as much else as possibleand natural) and elicit and measure the dependent variable to test our hypothesis thatthere is some relationship between them. Bivariate tabular analysis is good for askingthe following kinds of questions:

1. Is there a relationship between any two variables in the data?

2. How strong is the relationship in the data?

3. What is the direction and shape of the relationship in the data?

4. Is the relationship due to some Is the relationship due to some intervening variable(s)in the data?

To see any patterns or systematic relationship between biological sex of undergraduatesat University of X and reported footwear preferences, we could summarize our results ina table like this:

Table 1: Male and Female Undergraduate Footwear Preferences

Sandals Sneakers Leathershoes Boots Other

Male

Female

Depending upon how our 50 male and 50 female subjects responded, we could make adefinitive claim about the (reported) footwear preferences of those 100 people.

In constructing bivariate tables, typically values on the independent variable are arrayedon vertical axis, while values on the dependent variable are arrayed on the horizontalaxis. This allows us to read 'across' from hypothetically 'causal' values on the

independent variable to their 'effects', or values on the dependent variable How youarrange the values on each axis should be guided "iconically" by your researchquestion/hypothesis. For example, if values on an independent variable were arrangedfrom lowest to highest value on the variable and values on the dependent variable werearranged left to right from lowest to highest, a positive relationship would show up as arising left to right line. (But remember, association does not equal causation; anobserved relationship between two variables is not necessarily causal.)

Each intersection/cell-of a value on the independent variable and a value on theindependent variable-reports the result of how many times that combination of valueswas chosen/observed in the sample being analyzed. (So you can see that crosstabs arestructurally most suitable for analyzing relationships between nominal and ordinalvariables. Interval and ratio variables will have to first be grouped before they can "fit"into a bivariate table.) Each cell reports, essentially, how many subjects/observationsproduced that combination of independent and dependent variable values? So, forexample, the top left cell of the table above answers the question: "How many maleundergraduates at University of X prefer sandals?" (Answer: 6 out of the 50 sampled.)

Table 1b: Male and Female Undergraduate Footwear Preferences

Sandals Sneakers Leathershoes Boots Other

Male 6 17 13 9 5

Female 13 5 7 16 9

Reporting and interpreting cross tabs is the most easily done by converting rawfrequencies (in each cell) into percentages of each cell within the values or categories ofthe independent variable. For example, in the footwear preferences table above, totaleach row, then divide each cell by its own total, and multiply that faction by 100.

Table 1c: Male and Female Undergraduate Footwear Preferences(percentages)

Sandals Sneakers Leathershoes Boots Other N

Male 12 34 26 18 10 50

Female 26 10 14 32 18 50

Percentages basically standardize cell frequencies as if there were 100subjects/observations in each category of the independent variable. This is useful forcomparing across values on the independent variable, but that usefulness comes at theprice of a generalization--from the actual number of subjects/observations in that

column in your data to a hypothetical 100 subjects/observations. If the raw row totalwas 93, then percentages do little violence to the raw scores; but if the raw total is 9,then the generalization (on no statistical basis, i.e., with no knowledge of sample-population representativeness) is drastic. So you should provide that total N at the endof each row/independent variable category (for replicability and to enable the reader toassess your interpretation of the table's meaning).

With this caveat in mind, you can compare the patterns of distribution ofsubjects/observations along the dependent variable between the values of theindependent variable: e.g., compare male and female undergraduate footwearpreference. (For some data, plotting the results on a line graph can also help youinterpret the results: i.e., whether there is a positive (/), negative (), or curvilinear (/, /)relationship between the variables). Table 1c shows that within our sample, roughlytwice as many females preferred sandals and boots as males, and within our sample,about three times as many men preferred sneakers as women and twice as many menpreferred leather shoes. We might also infer from the 'Other' category that femalestudents within our sample had a broader range of footwear preferences than did malestudents.

Generalizing from Samples to Populations

Converting raw observed values or frequencies into percentages does allow us to seemore easily patterns in the data, but that is all we can see: what is in the data.

Knowing with great certainty the footwear preferences of a particular group of 100undergraduates at University of X is of limited use to us; we usually want to measure asample in order to know something about the larger populations from which oursamples were drawn. On the basis of raw observed frequencies (or percentages) of asamples behavior or characteristics, we can make claims about the sample itself, but wecannot generalize to make claims about the population from which we drew our sample,unless we submit our results to a test of statistical significance. A test of statisticalsignificance tells us how confidently we can generalize to a larger (unmeasured)population from a (measured) sample of that population.

How does chi square do this? Basically, the chi square test of statistical significance is aseries of mathematical formulas which compare the actual observed frequencies of somephenomenon (in our sample) with the frequencies we would expect if there were norelationship at all between the two variables in the larger (sampled) population. That is,chi square tests our actual results against the null hypothesis and assesses whether theactual results are different enough to overcome a certain probability that they are due tosampling error. In a sense, chi-square is a lot like percentages; it extrapolates apopulation characteristic (a parameter) from the sampling characteristic (a statistic)similarly to the way percentage standardizes a frequency to a total column N of 100. Butchi-square works within the frequencies provided by the sample and does not inflate (orminimize) the column and row totals.

Chi Square Requirements

As mentioned before, chi square is a nonparametric test. It does not require the sampledata to be more or less normally distributed (as parametric tests like t-tests do),although it relies on the assumption that the variable is normally distributed in thepopulation from which the sample is drawn.

But chi square does have some requirements:

1. The sample must be randomly drawn from the population.

As with any test of statistical significance, your data must be from a random sample ofthe population to which you wish to generalize your claims.

2. Data must be reported in raw frequencies (not percentages).

You should only use chi square when your data are in the form of raw frequency countsof things in two or more mutually exclusive and exhaustive categories. As discussedabove, converting raw frequencies into percentages standardizes cell frequencies as ifthere were 100 subjects/observations in each category of the independent variable forcomparability. Part of the chi square mathematical procedure accomplishes thisstandardizing, so computing the chi square of percentages would amount tostandardizing an already standardized measurement

3. Measured variables must be independent.

Any observation must fall into only one category or value on each variable. In ourfootwear example, our data are counts of male versus female undergraduates expressinga preference for five different categories of footwear. Each observation/subject iscounted only once, as either male or female (an exhaustive typology of biological sex)and as preferring sandals, sneakers, leather shoes, boots, or other kinds of footwear. Forsome variables, no 'other' category may be needed, but often 'other' ensures that thevariable has been exhaustively categorized. (For some kinds of analysis, you may need toinclude an "uncodable" category.) In any case, you must include the results for the wholesample.

4. Values/categories on independent and dependent variables must be mutuallyexclusive and exhaustive.

Furthermore, you should use chi square only when observations are independent: i.e.,no category or response is dependent upon or influenced by another. (In linguistics,often this rule is fudged a bit. For example, if we have one dependent variable/columnfor linguistic feature X and another column for number of words spoken or written(where the rows correspond to individual speakers/texts or groups of speakers/textswhich are being compared), there is clearly some relation between the frequency offeature X in a text and the number of words in a text, but it is a distant, not immediatedependency.)

5. Observed frequencies cannot be too small.

Chi-square is an approximate test of the probability of getting the frequencies you'veactually observed if the null hypothesis were true. It's based on the expectation thatwithin any category, sample frequencies are normally distributed about the expectedpopulation value. Since (logically) frequencies cannot be negative, the distributioncannot be normal when expected population values are close to zero-since the samplefrequencies cannot be much below the expected frequency while they can be muchabove it (an asymmetric/non-normal distribution). So, when expected frequencies arelarge, there is no problem with the assumption of normal distribution, but the smallerthe expected frequencies, the less valid are the results of the chi-square test. We'lldiscuss expected frequencies in greater detail later, but for now remember that expectedfrequencies are derived from observed frequencies. Therefore, if you have cells in yourbivariate table which show very low raw observed frequencies (5 or below), yourexpected frequencies may also be too low for chi square to be appropriately used. Inaddition, because some of the mathematical formulas used in chi square use division, nocell in your table can have an observed raw frequency of 0.

The following minimum frequency thresholds should be obeyed:

♦ for a 1 x 2 or 2 x 2 table, expected frequencies in each cell should be at least 5;

♦ for a 2 x 3 table, expected frequencies should be at least 2;

♦ for a 2 x 4 or 3 x 3 or larger table, if all expected frequencies but one are at least 5 andif the one small cell is at least 1, chi-square is still a good approximation.

In general, the greater the degrees of freedom (i.e., the more values/categories on theindependent and dependent variables), the more lenient the minimum expectedfrequencies threshold. (We'll discuss degrees of freedom in a moment.)

Collapsing Values

A brief word about collapsing values/categories on a variable is necessary. First,although categories on a variable, especially a dependent variable, may be collapsed,they cannot be excluded from a chi-square analysis. That is, you cannot arbitrarilyexclude some subset of your data from your analysis. Second, a decision to collapsecategories should be carefully motivated, with consideration for preserving the integrityof the data as it was originally collected. (For example, how could you collapse thefootwear preference categories in our example and still preserve the integrity of theoriginal question/data? You can't, since there's no way to know if combining, e.g., bootsand leather shoes versus sandals and sneakers is true to your subjects' typology offootwear.) As a rule, you should perform a chi square on the data in its uncollapsedform; if the chi square value achieved is significant, then you may collapse categories totest subsequent refinements of your original hypothesis.

Computing Chi Square

Let’s walk through the process by which a chi square value is computed, using Table 1babove (renamed Table 1d below).

The first step is to determine our threshold of tolerance for error. That is, what odds arewe willing to accept that we are wrong in generalizing from the results in our sample tothe population it represents? Are we willing to stake a claim on a 50 percent chance thatwe're wrong? a 10 percent chance? a five percent chance? 1 percent? The answerdepends largely on our research question and the consequences of being wrong. Ifpeople's lives depend on our interpretation of our results, we might want to take only 1chance in 100,000 (or 1,000,000) that we're wrong. But if the stakes are smaller, forexample, whether or not two texts use the same frequencies of some linguistic feature(assuming this is not a forensic issue in a capital murder case!), we might accept agreater probability--1 in 100 or even 1 in 20 - that our data do not represent thepopulation we're generalizing about. The important thing is to explicitly motivate yourthreshold before you perform any test of statistical significance, to minimize anytemptation for post hoc compromise of scientific standards. For our purposes, we'll set aprobability of error threshold of 1 in 20, or p < .05, for our Footwear study).

The second step is to total all rows and columns.

Table 1d: Male and Female Undergraduate Footwear Preferences: ObservedFrequencies with Row and Column Totals

Sandals Sneakers Leathershoes Boots Other Total

Male 6 17 13 9 5 50

Female 13 5 7 16 9 50

Total 19 22 20 25 14 100

Remember, that chi square operates by comparing the actual, or observed frequencies ineach cell in the table to the frequencies we would expect if there were no relationship atall between the two variables in the populations from which the sample is drawn. Inother words, chi square compares what actually happened to what hypothetically wouldhave happened if ‘all other things were equal' (basically, the null hypothesis). If ouractual results are sufficiently different from the predicted null hypothesis results, we canreject the null hypothesis and claim that a statistically significant relationship existsbetween our variables.

Chi square derives a representation of the null hypothesis—the 'all other things beingequal' scenario—in the following way. The expected frequency in each cell is the productof that cell's row total multiplied by that cell's column total, divided by the sum total ofall observations. So, to derive the expected frequency of the "Males who prefer Sandals"cell, we multiply the top row total (50) by the first column total (19) and divide thatproduct by the sum total 100: (50 X 19)/100 = 9.5. The logic of this is that we are

deriving the expected frequency of each cell from the union of the total frequencies ofthe relevant values on each variable (in this case, Male and Sandals), as a proportion ofall observed frequencies (across all values of each variable). This calculation isperformed to derive the expected frequency of each cell, as shown in Table 1e below (thecomputation for each cell is listed below:

(Notice that because we originally obtained a balanced male/female sample, our maleand female expected scores are the same. This usually will not be the case.)

We now have a comparison of the observed results versus the results we would expect ifthe null hypothesis were true. We can informally analyze this table, comparing observedand expected frequencies in each cell (Males prefer sandals less than expected), acrossvalues on the independent variable (Males prefer sneakers more than expected, Femalesless than expected), or across values on the dependent variable (Females prefer sandalsand boots more than expected, but sneakers and shoes less than expected). But so far,the extra computation doesn't really add much more information than interpretation ofthe results in percentage form. We need some way to measure how different our

observed results are from the null hypothesis. Or, to put it another way, we need someway to determine whether we can reject the null hypothesis, and if we can, with whatdegree of confidence that we're not making a mistake in generalizing from our sampleresults to the larger population.

Logically, we need to measure the size of the difference between the pair of observedand expected frequencies in each cell. More specifically, we calculate the differencebetween the observed and expected frequency in each cell, square that difference, andthen divide that product by the difference itself. The formula can be expressed as:

(O - E)2 / E

Squaring the difference ensures a positive number, so that we end up with an absolutevalue of differences. If we didn't work with absolute values, the positive and negativedifferences across the entire table would always add up to 0. (You really understand thelogic of chi square if you can figure out why this is true.) Dividing the squared differenceby the expected frequency essentially removes the expected frequency from theequation, so that the remaining measures of observed/expected difference arecomparable across all cells.

So, for example, the difference between observed and expected frequencies for theMale/Sandals preference is calculated as follows:

1. Observed (6) - Expected (9.5) = Difference (-3.5)

2. Difference (-3.5) squared = 12.25

3. Difference squared (12.25) divided by Expected (9.5) = 1.289

The sum of all products of this calculation on each cell is the total chi square value forthe table. The computation of chi square for each cell is listed below:

(Again, because of our balanced male/female sample, our row totals were the same, sothe male and female observed – expected frequency differences were identical. This isusually not the case)

The total chi square value for Table 1 is 14.026.

Interpreting the Chi Square Value

We now need some criterion or yardstick against which to measure the table's chi squarevalue, to tell us whether or not it is significant. What we need to know is the probabilityof getting a chi square value of a minimum given size even if our variables are notrelated at all in the larger population from which our sample was drawn. That is, weneed to know how much larger than 0 (the absolute chi square value of the nullhypothesis) our table's chi square value must be before we can confidently reject the nullhypothesis. The probability we seek depends in part on the degrees of freedom of thetable from which our chi square value is derived.

Degrees of freedom

Mechanically, a table's degrees of freedom (df) can be expressed by the followingformula: df = (r - 1)(c - 1)

That is, a table's degrees of freedom equals the number of rows in the table minus onemultiplied by the number of columns in the table minus one (for 1 x 2 table, df = k - 1,where k = number of values/categories on the variable).

‘Degrees of freedom’ is an issue because of the way in which expected values in each cellare computed from the row and column totals of each cell. All but one of the expectedvalues in a given row or column are free to vary (within the total observed-and thereforeexpected) frequency of that row or column); once the free to vary expected cells arespecified, the last one is fixed by virtue of the fact that the expected frequencies mustadd up to the observed row and column totals (from which they are derived).

Another way to conceive of a table's degrees of freedom is to think of one row and onecolumn in the table as fixed, with the remaining cells free to vary. Consider the followingvisuals (where X = fixed):

df = (r – 1) (c – 1) = (3 – 1) (2 – 1) = 2 x 1 = 2

df = (r – 1) (c – 1) = (5 – 1) (3 – 1) = 4 x 2 = 8

So, for our Table 1,

Table 1: Male and Female Undergraduate Footwear Preferences

Sandals Sneakers Leathershoes Boots Other

Male X X X X X

Female X

df = (2 - 1) (5 – 1) = 1 x 4 = 4

In a statistics book, the sampling distribution of chi square (also known as critical valuesof chi squares typically listed in an appendix. You read down the column representingyour previously chosen probability of error threshold (e.g., p < 0.5) and across the rowrepresenting the degrees of freedom in your table. If your chi square value is larger thanthe critical value in that cell, your data presents a statistically significant relationshipbetween the variables in your table.

Table 1’s chi square value of 14.026 with 4 degrees of freedom, handily clears the relatedcritical value of 9.49, so we can reject the null hypothesis and affirm the claim that maleand female undergraduates at University of X differ in their (self-reported) footwearpreferences.

Statistical significance does not help you to interpret that nature or explanation of thatrelationship; that must be done by other means (including bivariate tabular analysis ofthe data). But a statistically significant chi square value does denote the degree ofconfidence you may hold that the relationship between variables described in yourresults is systematic in the larger population and not attributable to random error.

Statistical significance also does not ensure substantive significance. A large enoughsample may demonstrate a statistically significant relationship between two variables,but that relationship may be trivially weak one. Statistical significance means only thatthe pattern of distribution and relationship between the variables which is found in thedata from a sample can be confidently generalized to the larger population from whichthe sample was randomly drawn. By itself it does not ensure that the relationship istheoretically or practically important, or even very large.

Measures of Association

While the issue of theoretical or practical importance of a statistically significant resultcannot be quantified, the relative magnitude of a statistically significant relationship canbe measured. Chi Square allows you to make decisions about whether there is arelationship between two or more variables; if the null hypothesis is rejected, weconclude that there is a statistically significant relationship between the variables. Butwe frequently want a measure of the strength of that relationship - an index of degree ofcorrelation, a measure of the degree of association between the variables represented inour table (and data). Luckily, several measures of association can be derived from atable’s chi square value.

For tables larger than 2 x 2 (like our Table 1), a measure called 'Cramer's phi' is derivedby the following formula (where N is the total number of observations, and k is thesmaller of the number of rows or columns).

Cramer’s phi = sqrt [(chi square) / (N x (k-1)]

So, for our Table 1 (2 x 5), Cramer’s phi will be computed as follows:

1. N (k - 1) = 100 (2 – 1) = 100

2. Chi square / 100 = 14.026 / 100 = 0.14

3. Square root of 0.14 = 0.37

The product is interpreted as a Pearson r (that is, as a correlation coefficient).

(For 2X2 tables, a measure called 'phi' is derived by dividing the table's chi square valueby N (the total number of observations) and then taking the square root of the product.Phi is also interpreted as a Pearson r.)

A complete account of how to interpret correlation coefficients is unnecessary forpresent purposes. It will suffice to say that r2 is a measure called shared variance.Shared variance is the portion of the total behavior (or distribution) of the variablesmeasured in the sample data which is accounted for by the relationship we've alreadydetected with our chi square. For Table 1, r2 = 0.137, so approximately 14% of the totalfootwear preference story is explained/predicted by biological sex.

Computing a measure of association like phi or Cramer's phi is rarely done inquantitative linguistic analyses, but it is an important benchmark of just 'how much' ofthe phenomenon under investigation has been explained. For example, Table 1'sCramer's phi of 0.37 (r2 = 0.137) means that there are one or more, variables stillundetected which, cumulatively, account for and predict 86% of footwear preferences.This measure, of course, doesn't begin to address the nature of the relation(s) betweenthese variables, which is a crucial part of any adequate explanation or theory.

SUMMARY

The above chapter has given the framework for performing key statistical tests like chi-square test. Chi-square is a non parametric test of statistical significance for bivariatetabular analysis.

KEY WORDS

· Bivariate tabular analysis· Chi square test· Measure of association· Degrees of freedom

IMPORTANT QUESTIONS

1. What do you mean by bivariate tabular analysis?

2. What are the statistical applications in chi square tests?

3. How will you calculate the degree of freedom?

- End of Chapter -

LESSON - 8

T-TEST, F-TEST

OBJECTIVES

· To know the significance of statistical list· To find out the details of F-test and T-test· To learn the detailed procedures for doing above mentioned test.

STRUCTURE

· F-test· Cumulative probability and F distribution· F-Test for equality· T-test· Two sample t-test for equal means.

F-TEST

The f statistic, also known as an f value, is a random variable that has an F distribution.

The F Distribution

The distribution of all possible values of the f statistic is called an F distribution, with v1

= n1 – 1 and v2 = n2 – 1 degrees of freedom.

The curve of the F distribution depends on the degrees of freedom, v1 and v2. Whendescribing an F distribution, the number of degrees of freedom associated with thestandard deviation in the numerator of the f statistic is always stated first. Thus, f(5,9)would refer to an F distribution with v1 = 5 and v2 = 9 degrees of freedom; whereas f(9,5)would refer to an F distribution with v1 = 9 and v2 = 5 degrees of freedom. Note that thecurve represented by f(5,9) would differ from the curve represented by f(9,5).

The F distribution has the following properties:

♦ The mean of the distribution is equal to v1 / (v2 – 2)

♦ The variance is equal to

v22 (v1 + 2)

----------------------------

v1 (v2 – 2) (v2 – 4)

Cumulative Probability and the F Distribution

Every f statistic can be associated with a unique cumulative probability. This cumulativeprobability represents the likelihood that the f statistic is less than or equal to a specifiedvalue. Here are the steps required to compute an f statistic:

1. Select a random sample of size n1 from a normal population, having a standarddeviation equal to σ1

2. Select an independent random sample of size n2 from a normal population, having astandard deviation equal to σ2

The f statistic is the ratio of and s12/σ12 and s22/σ22

The following equivalent equations are commonly used to compute an f statistic:

f = [s12 / σ12] / [s22 / σ22]

f = [s12 x σ22] / [s22 x σ12]

f = [X12 / v1] / [X22 / v2]

f = [X12 x v2] / [X22 x v1]

where

σ1 = standard deviation of population 1

s1 = standard deviation of the sample drawn from population 1

σ2 = standard deviation of population 2

s2 = standard deviation of the sample drawn from population 2

X12 = chi-square static for the sample drawn from population 1

v1 = degrees of freedom for X12

X22 = chi-square statistic for the sample drawn from population 2

v2 = degrees of freedom for X22

Degrees of freedom v1 = n1 - 1, and

Degrees of freedom v2 = n2 – 1.

Sample Problems

Example

Suppose you randomly select 7 women from a population of women and 12 men from apopulation of men. The table below shows the standard deviation in each sample and ineach population.

Compute the f statistic.

Solution

The f statistic can be computed from the population and sample standard deviations,using the following equation:

f = [s12 / σ12] / [s22 / σ22]

where,

σ1 is the standard deviation of population 1

s1 = standard deviation of the sample drawn from population 1

σ2 = standard deviation of population 2

s2 = standard deviation of the sample drawn from population 2

As you can see from the equation, there are actually two ways to compute an f statisticfrom these data. If the women's data appears in the numerator, we can calculate an fstatistic as follows:

f = (35 / 30) / (45 / 50) = 1.66667 / 0.9 = 1.85

On the other hand, if the men's data appears in the numerator, we can calculate an fstatistic as follows:

f = (45 / 50) / (35 / 30) = 0.9 / 1.66667 = 0.54

This example illustrates the importance of specifying the degrees of freedom associatedwith the numerator and denominator of an f statistic. This topic is continued in the nextexample.

F-Test for Equality of Two Standard Deviations

An F-test (Snedecor and Cochran, 1983) is used to test if the standard deviations of twopopulations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the standard deviations are not equal.The one-tailed version only tests in one direction, that is, the standard deviation fromthe first population is either greater than or less than (but not both) the secondpopulation standard deviation. The choice is determined by the problem. For example, ifwe are testing a new process, we may only be interested in knowing if the new process isless variable than the old process.

We are testing the hypothesis that the standard deviations for sample one and sampletwo are equal. The output is divided into four sections.

1. The first section prints the sample statistics for sample one used in the computation ofthe F-test.

2. The second section prints the sample statistics for sample two used in thecomputation of the F-test

3. The third section prints the numerator and denominator standard deviations, the F-test statistic value, the degrees of freedom, and the cumulative distribution function(cdf) value of the F-test statistic. The F-test statistic cdf value is an alternative way ofexpressing the critical value. This cdf value is compared to the acceptance intervalprinted in section four. The acceptance interval for a two-tailed test is (0,1–α)

4. The fourth section prints the conclusions for a 95% test since this is the most commoncase. Results are printed for an upper one-tailed test. The acceptance interval column isstated in terms of the cdf value printed in section three. The last column specifieswhether the null hypothesis is accepted or rejected. For a different significance level, theappropriate conclusion can be drawn from the F-test statistic cdf value printed insection four. For example, for a significance level of 0.10, the corresponding acceptanceinterval become (0.000,0.9000).

The F-test can be used to answer the following questions:

1. Do two samples come from populations with equal standard deviations?

2. Does a new process, treatment, or test reduce the variability of the current process?

T-TEST

We have seen that the central limit theorem can be used to describe the samplingdistribution of the mean, as long as two conditions are met:

1. The sample size must be sufficiently large (at least 30).

2. We need to know the standard deviation of the population, which is denoted by α.

But sample sizes are sometimes small and often we do not know the true populationstandard deviation. When either of these problems occurs, statisticians rely on thedistribution of the t statistic (the t-score), whose values are given by:

T = [x – μ] / [s / sqrt(n)]

where,

x = sample mean

μ = population mean

s = standard deviation of the sample

n = sample size

The distribution of this t statistic is called the t-distribution or the Student t-distribution. The t-distribution can be used whenever samples are drawn frompopulations possessing a bell-shaped distribution (i.e., approximately normal).

The t-distribution has the following properties

· The mean of the distribution is equal to 0.· The variance is equal to v / (v - 2), where v is the degrees of freedom (see next

section) and v > 2.

Parametric tests provide inferences for making statements about the means of parentpopulations. A t-test is commonly used for this purpose. This test is based on theStudent's t statistic. The t statistic assumes that the variable is normally distributed, themean is known (or assumed to be known), and the population variance is estimatedfrom the sample. Assume that the random variable X is normally distributed, with meanμ and unknown population variance σ2, which is estimated by the sample variance S2.Recall that the standard deviation of the sample mean, X, is estimated as sx = s/n. Then,t = (X - μ) / sx is distributed with n - 1 degrees of freedom.

The t-distribution is similar to the normal distribution in appearance. Both distributionsare bell-shaped and symmetric. However, as compared to the normal distribution, thatdistribution has more area in the tails and less in the center. This is because populationvariance σ2 is unknown and is estimated by the sample variance S2. Given theuncertainty in the value of S2, the observed values of t are more variable than those of z.Thus we must go a large number of standard deviations from 0 to encompass a certainpercentage of values from the t distribution than is the case with the normaldistribution. Yet, as the number of freedom increases, the t distribution approaches thenormal distribution. In large samples of 120 or more, the t distribution and the normaldistribution are virtually indistinguishable. Table 4 in the statistical appendix shows

selected percentiles of the t distribution. Although normality is assumed, the t test isquite robust to departures from normality.

The procedure for hypothesis testing, for the special case when the t statistic is used, isas follows:

1. Formulate the null (H0) and the alternative (H1) hypotheses.

2. Select the appropriate formula for the t statistic.

3. Select a significance level, a, for testing H0. Typically, the 0.05 level is selected.

4. Take one or two samples and compute the mean and standard deviation for eachsample.

5. Calculate the t statistic assuming H0 is true.

6. Calculate the degrees of freedom and estimate the probability of getting a moreextreme value of the statistic from Table 4. (Alternatively, calculate the critical value ofstatistic.)

7. If the probability computed in step 6 is smaller than the significance level selected inreject H0. If the probability is larger, do not reject H0. (Alternatively, if the valuecalculated t statistic in step 5 is larger than the critical value determined in step 6, rejectH0. If the calculated value is smaller than the critical value, do not reject H0). To rejectH0 does not necessarily imply that H0 is true. It only means that the result is notsignificantly different than that assumed by H0.

8. Express the conclusion reached by the t-test in terms of the marketing researchproblem.

Degrees of Freedom

There are actually many different t distributions. The particular form of the tdistribution is determined by its degrees of freedom. The degree of freedom refers to thenumber of independent observations in a sample.

The number of independent observations is often equal to the sample size minus one.Hence, the distribution of the t statistic from samples of size 8 would be described by a tdistribution having (8 – 1) = 7 degrees of freedom. Similarly, a t-distribution having 15degrees of freedom would be used with a sample of size 16.

The t-distribution is symmetrical with a mean of zero. Its standard deviation is alwaysgreater than 1, although it is close to 1 when there are many degrees of freedom. Withinfinite degrees of freedom, the t distribution is the same as the standard normaldistribution.

Sampling Distribution of the Mean

When the sample size is small (< 30), the mean and standard deviation of the samplingdistribution can be described as follows:

μx = μ and σx = s * sqrt[1/n – 1/N]

where,

μx = mean of the sampling distribution

μ = mean of the population

σx = standard error (i.e., the standard deviation of the sampling distribution)

s = standard deviation of the sample

n = sample size

N = population size

Probability and the Student t Distribution

When a sample of size n is drawn from a population having a normal (or nearly normal)distribution, the sample mean can be transformed into a t score, using the equationpresented at the beginning of this lesson. We repeat that equation here: T = [x – μ] / [s /sqrt(n)]

where,

x = sample mean

μ = population mean

s = standard deviation of the sample

n = sample size

The degrees of freedom = n - 1

Every t score can be associated with a unique cumulative probability. This cumulativeprobability represents the likelihood of finding a sample mean less than or equal to x,given a random sample of size n.

Two-sample F-Test for Equal Means

The two-sample t-test (Snedecor and Cochran, 1989) is used to determine if twopopulation means are equal. A common application of this is to test if a new process ortreatment is superior to a current process or treatment.

There are several variations on this test:

1. The data may either be paired or not paired. By paired, we mean that there is a one-to-one correspondence between the values in the two samples. That is, if X1, X2,… , Xn

and Y1, Y2... , Yn are the two samples, then Xi corresponds to Yi. For paired samples, thedifference Xi - Yi is usually calculated. For unpaired samples, the sample sizes for thetwo samples may or may not be equal. The formulas for paired data are somewhatsimpler than the formulas for unpaired data.

2. The variances of the two samples may be assumed to be equal or unequal. Equalvariances yield somewhat simpler formulas, although with computers this is no longer asignificant issue.

In some applications, you may want to adopt a new process or treatment only if itexceeds the current treatment by some threshold. In this case, we can state the nullhypothesis in the form that the difference between the two populations means is equalto some constant (μ1 – μ2 = d0) where the constant is the desired threshold.

Interpretation of Output

1. We are testing the hypothesis that the population mean is equal for the two samples.The output is divided into five sections.

2. The first section prints the sample statistics for sample one used in the computationof the f-test

3. The second section prints the sample statistics for sample two used in thecomputation of the t-test.

4. The third section prints the pooled standard deviation, the difference in the means,the t-test statistic value, the degrees of freedom, and the cumulative distributionfunction (cdf) value of the t-test statistic under the assumption that the standarddeviations are equal. The t-test statistic cdf value is an alternative way of expressing thecritical value. This cdf value is compared to the acceptance intervals printed in sectionfive. For an upper one-tailed test, the acceptance interval is (0,1-α), the acceptanceinterval for a two-tailed test is (α/2, 1- α/2), and the acceptance interval for a lower one-tailed test is (α,1).

5. The fourth section prints the pooled standard deviation, the difference in the means,the t-test statistic value, the degrees of freedom, and the cumulative distributionfunction (cdf) value of the t-test statistic under the assumption that the standarddeviations are not equal. The t-test statistic cdf value is an alternative way of expressingthe critical value. cdf value is compared to the acceptance intervals printed in section

five. For an upper one-tailed test, the alternative hypothesis acceptance interval is (1-α,1), the alternative hypothesis acceptance interval for a lower one-tailed test is (0,α), andthe alternative hypothesis acceptance interval for a two-tailed test is (1-α/2,1) or (0,α/2).Note that accepting the alternative hypothesis is equivalent to rejecting the nullhypothesis.

6. The fifth section prints the conclusions for a 95% test under the assumption that thestandard deviations are not equal since a 95% test is the most common case." Resultsare given in terms of the alternative hypothesis for the two-tailed test and for the one-tailed test in both directions. The alternative hypothesis acceptance interval column isstated in terms of the cdf value printed in section four. The last column specifieswhether the alternative hypothesis is accepted or rejected. For a different significancelevel, the appropriate conclusion can be drawn from the t-test statistic cdf value printedin section four. For example, for a significance level of 0.10, the correspondingalternative hypothesis acceptance intervals are (0,0.05) and (0.95,1), (0,0.10), and(0.90,1).

Two-sample f-tests can be used to answer the following questions

1. Is process 1 equivalent to process 2?

2. Is the new process better than the current process?

3. Is the new process better than the current process by at least some pre-determinedthreshold amount?

Matrices of t-tests

T-tests for dependent samples can be calculated for long lists of variables, and reviewedin the form of matrices produced with case wise or pair wise deletion of missing data,much like the correlation matrices. Thus, the precautions discussed in the context ofcorrelations also apply to t-test matrices:

a. The issue of artifacts caused by the pair wise deletion of missing data in t-tests and

b. The issue of "randomly" significant test values.

SUMMARY

The above chapter has given the frame work for performing key statistical tests like F-Test and T-test. T-test and F-test are parametric tests. T-test is any statistical hypothesistest in which the test statistic has a Student’s distribution if the null hypothesis is true.

KEY TERMS

· Degrees of Freedom· T test

· T distribution· F distribution· Sampling distribution

IMPORTANT QUESTIONS

1. How will you calculate the Degrees of Freedom?

2. Explain the procedures for performing t test?

3. What are the metrics of t test?

4. Explain the procedures for performing f test?

REFERENCE

1. Sumathi, S. and P. Saravanavel - Marketing research and Consumer Behaviour

2. Ferber, R., and Verdoorn, P.J., Research Methods in Business, New York-theMacmillan Company 1962.

3. Ferber, R., Robert (ed.) Hand Book of Marketing Research. New York McGraw Hill,Inc. 1948.

- End of Chapter -

LESSON – 9

METHODS OF DATA COLLECTION

OBJECTIVES

· To know the different types of Data and the sources of the same.· To learn the different data collection methods and its merits, demerits.· To understand the difference between Questionnaire and Interview Schedule.· To apply the suitable data collection method for the research.

STRUCTURE

· Primary data· Secondary data· Interview· Questionnaire

· Observation

INTRODUCTION

After defining the research problem and drawing the research design, the importanttask of the researcher is Data collection. While deciding on the research method, themethod of data collection to be used for the study also should be planned.

The same of information and the manner in which data are collected could well make abig difference to the effectiveness of the research project.

In data collection, the researcher should be very clear on what type of data is to be usedfor the research. There are two types of data namely primary data and secondary data.The method of collecting primary and secondary data differ since primary data are to beoriginally collected while in case of secondary data, it is merely compilation of theavailable data.

PRIMARY DATA

Primary data are generally, information gathered by the researcher for the purpose ofthe project at hand. When the data are collected for the first time using experiments andsurveys, the data is known as primary data. So, in case of primary data, it is always theresponsibility of the researcher to decide on further processing of data.

There are several methods of data collection each with its advantages anddisadvantages.

The data collection methods include the following:

1. Interview- Face to face interview, Telephone interview, Computer assignedinterview, Interviews through electronic media

2. Questionnaire - These are personally administered sent through the mail, orelectronically administered

3. Observation - of individuals and events with or without video taping or audiorecording. Hence interviews, questionnaires and observation methods are three maindata collection methods.

Some of the other data collection methods used to collect primary data:

1. Warranty cards

2. Distributor Audits

3. Pantry Audits

4. Consumer Panels

SECONDARY DATA

As already mentioned, it the researcher who decides to collect secondary data for hisresearch that can be collected through various sources. In the case of secondary data,the researcher may not face severe problems that are usually associated with primarydata collection.

Secondary data may either be published or unpublished data. Published data may beavailable with the following sources:

1. Various publications of the central, state or local governments.

2. Various publications of foreign governments or of international bodies.

3. Technical and Trade Journals.

4. Books, Magazines, Newspapers.

5. Reports and publication from various associations connected with industry andbusiness.

6. Public records and statistics.

7. Historical documents.

Though there are various sources for secondary data, it is the responsibility of theresearcher that he should make a minute scrutiny of data in order to involve the datamore suitable and adequate.

INTERVIEWS

An interview is a purposeful discussion between two or more people. Interview can helpto gather valid and reliable data. There are several types of interviews.

Types of Interviews

Interviews may be conducted in a very formal manner, using structured andstandardized questionnaire for each respondent.

Interviews also may be conducted informally through unstructured conversation. Basedon formal nature and structure, the interviews are classified as follows:

1. Structured Interviews : These interviews involve the use of a set of predeterminedquestions and of highly standardized techniques of recording. So, in this type ofinterview a rigid proved method is followed.

2. Semi Structured interviews : These interviews may have a structuredquestionnaire but the technique of interviewing may not have a proved method. Theseinterviews have more scope for discussion and recording of respondent's opinion andviews.

3. Unstructured Interviews : These interviews neither follow a system of pre-determined questions nor a standardized technique of recording information. But theunstructured interviews need an in depth knowledge and greater skill on the part of theinterviewers.

All the three types of interviews may be conducted by the interviewer by askingquestions generally in face to face contact. These interviews may take a form of directpersonal investigation or may be indirect oral investigation. In case of direct personalinvestigation, the interviewer has to collect the information personally. So, it is the dutyof interviewer to be there in the spot to meet the respondents to collect data.

When this is not possible the interviewer may have to cross examine others who aresupposed to have knowledge about the problem and here information may be recorded.

Example: Commissions and committee appointed by Government. Depending on theapproaches of the interviewer, the interviews may be classified as:

1. Non-directive interviews : In these types of interviews, the interviewer is verymuch free to arrange the form and order of questions. The questionnaire for these kindsof interviews also may contain open ended questions where in the respondent also feelfree to respond to the questions.

2. Directive interviews : This is also a type of structured interview. In this method apredetermined questionnaire is used and the respondent is express to limit the answersonly to the question asked. Market surveys and interviews by news papercorrespondents are the suitable examples.

3. Focused interviews : These methods of interviews are in between directive andnon - directive. Here the methods are neither fully standardized nor non-standardized.Here the objective is to focus the attention of the respondents on a specific issue orpoint. Example: A detective questioning a person regarding a crime committed in anarea.

4. In-depth interviews : In these interview methods, the respondents are encouragedto express his thoughts on the topic of the study. In depth interviews are conducted toget important aspects of psycho - social situations, which are otherwise not readilyevident.

The major strength of these kinds of interviews is their capacity to uncover the basic andcomplete answers to the questions asked.

Advantages of interviews

Despite the variations in interviews techniques the following are the advantages of thesame.

1. Interviews may help to collect more information and also in depth information.

2. The unstructured interviews are more advantages since, there is always anopportunity for the interviewers to restructure the questions.

3. Since the respondents are contacted for the information, there are always greateradvantages of creating support and collecting personal information also.

4. Interviews help the researcher to collect all the necessary information, here theevidence no response will be very low.

5. It is also possible for the interviewer to collect additional information about theenvironment, name, behavior and attitude of the respondents.

Disadvantages of interviews

1. Interviews are expensive methods especially in case of widely spread geographicalsamples are taken.

2. There may be a possibility for the barriers in the case of both interviewer and therespondent.

3. These methods are also time-consuming especially when the large samples are takenfor the study.

4. There may be a possibility for the respondent to hide the real opinion, so genuine datamay not be collected.

5. Sometimes there will be great difficult in adopting interview methods became fixingappointment with the respondent itself may not be possible.

Hence, for successful implementation of the interview method, the interviewer shouldbe carefully selected, trained and briefed.

How to make interviews successful?

1. As mentioned above, the interviewers must be carefully selected and trained properly.

2. The interviewer should have the knowledge of exploring to collect the neededinformation from the respondent.

3. Honesty and integrity of the interviewer also determines the outcomes of theinterview.

4. The support with the respondent should be created by the interviewer.

5. Qualities such as politeness, courteousness friendly and conversational are necessaryto make the interview successful.

Telephonic Interviews

A part from all the above the telephonic interviews are also conducted to collect thedata. Respondents are contacted over the phone to gather data. Telephonic interviewsare more flexible in timing - it is faster than other methods and this method is cheapermethod also. For these sorts of interviews no field's staff is required and also theinformation can be recorded without causing embarrassment to respondents especiallywhen very personal questions are asked. But these methods are much restricted to therespondents who have telephone facility. Possibility for the biased replies is relativelymore and since there is not personal touch by both there is a greater possibility for nonanswered questions.

QUESTIONNAIRES

Questionnaires are widely used for data collection in social sciences, researchparticularly in surveys. This is been accepted as a reliable not for gathering data fromlarge, diverse and scattered social groups. Bogardus describes the questionnaire as a listof questions sent to a number of persons for their answers and which obtains standardsresults that can be tabulated and treated statistically.

There are two types of questionnaires, also which are structured and unstructured.The design of the questionnaire may vary based on the way it is administered. Thequestionnaire methods are most extensively used in economic and business surveys.

Structured questionnaire

These contain definite concrete and preordained questions. The answer collected usingthis structured questionnaire is very precise and there is no vagueness and ambiguity.

The structured questionnaire may have the following types:

1. Closed - form questionnaire: Questions are set in such a way that leaves only fewalternative answers. Example: Yes / No type questions.

2. Open - ended questionnaire: Here the respondent has the choice of using his ownstyle, expression of language, length and perception. The respondents are not restrictedin his replies.

Unstructured questionnaire

The questions in this questionnaire are not structured in advance. These sorts ofquestionnaire give more scopes for variety of answers. Mainly to conduct interviewswhere in different responses are expected, these type of questionnaire are used.

The researcher should be much clear on when to use the questionnaire. These can bemostly used in case of descriptive and explanatory type of research. Example:Questionnaire on attitude, opinion, and organizational practices, enable the researcherto identify and describe the variability.

Advantages of the Questionnaire

· Cost involved is low in case of widely spread geographical sample.· It is more appreciable one because it more free from the subjectivity of the

interviews.· Respondents also may find adequate time to give well thought answers.· It is more advantages in the case when respondents are not reachable.

But the rate of return of questionnaire and the fulfillment at needed data for the studymay be doubtful. This can be used only when the respondents are educated and willknow to read the language in which questionnaire is prepared. Possibilities forambiguous replies, omission of replies are more. This method is more time consuming.

Before sending the final questionnaire to the respondents it is always more important toconduct the Pilot study for resting the questionnaire. Pilot study is just a rehearsal of themain survey such survey conducted with help of experts brings more strength to thequestionnaire.

Data collection through schedules

This method is very much like data collection through questionnaires. Schedules are aproforma containing set of questions which are filled in by the enumerators who arespecially appointed for this purpose. In this method the enumerators are expected toperform well and they must be knowledgeable and must possess the capacity of crossexamination in order to find the truth. These methods are usually expensive and areconducted by bigger and Government organizations.

OBSERVATION

Observation is one of the cheaper and effective techniques of data collection. Theobservation is understood as a systematic process of recording the behavioral patternsof people, objects and occurrence as they are witnessed.

Using this observational method of data collection the following data related tomovements, work habits, the statements mad and meetings conducted,[by humanbegins] facial expressions, body language and other emotions such as joy, anger andsorrowfulness of the human beings can be collected.

Also other environmental factors includes layout, workflow patterns, physicalarrangements can also be noted. In this method of data collection the investigatorcollects the data without interacting with the respondents. Example: Instead of askingabout the brands of shirts or the program they watch on just observing their pattern.

The observation would be classified based on the role of researcher as:

1. Non participant observation

The role of the investigator here would be an external agent who sits in a corner withoutinteracting with the samples which is to be observed.

2. Participant observation

Joins with the group and work along with them in way the work is done but many not beasking questions related to the research / investigation.

It also can be classified based on the methods as:

1. Structured observation

In this case the researcher may have a predetermined set of categories of activities orphenomena planned to be studied. Example: To observe the behavior pattern ofindividual when he/she go for purchasing to be planned in such a way where thefrequency of purchasing, and the interest during the purchase and the way goods arepreferred / selected. Any researcher would be having a plan on the observation to bemade.

2. Unstructured observation

The researcher may not do the data collection based on the specific ideas. These sorts ofmethods are used more qualitative research studies.

Example: To observe the behavior pattern of individual when he/she go for purchasingto be planned in such a way where the frequency of purchasing, and the interest duringthe purchase and the way goods are preferred / selected.

Merits of observational studies

· The data collected in this method are generally reliable and they are free fromrespondent's bias.

· It is easier to observe the busy people rather meeting and collecting the data.

Demerits of observational studies

· The observer has to be present in the situation where the data to be collected.· This method is very slow and expensive.

· Since the observer is going to collect the data by consuming more time andobserving the sample there is a possibility for biased information.

Survey Method

Survey is a popular method of "fact-finding" study which involves collection of datadirectly from the population at a particular time. Survey can be defined as a researchtechnique in which information may be gathered from a sample of people by use ofquestionnaire or interview.

Survey is considered as field study which is conducted in a natural setting which collectsinformation directly from the respondents. Surveys are been conducted for manypurposes - population census, socio economic surveys, expenditure surveys andmarketing surveys. The purpose of these surveys would be providing information to thegovernment planners or business enterprises. The surveys are also conducted to explainphenomena where in causal relationship between two variables to be assessed.

Surveys are been used to compare the demographic groups such as to compare the highand low income groups, to compare the preference based on age. These surveys are beenconducted in the care of descriptive type of research and in which large samples arefocused.

The surveys are more appropriate in the social and behavioral science. Surveys are moreconvened with formulating the hypothesis and testing the relationship between non-manipulated variables. The survey research requires skillful workers to gather data.

The subjects for surveys may be classified as:

1. Social surveys which include

· Demographic characteristics of a group of people· The social environment of people· People's opinion & attitudes

2. Economic surveys

· Economic conditions of people· Operations of economic system

Important stages in survey methods

Selecting the universe of the field

↓

Choosing samples from the universe

↓

Deciding on tools used for data collection

↓

Analyzing the data

Other methods of Data Collection

Warranty cards : A type of post card with few focused typed questions may be used bythe dealers / retailers to collect information from the customers. The dealers /researchers may request customers to fill in the required data.

Distributor Audits : These sorts of data may be collected by distributors to estimatethe market size, market share and seasonal purchasing pattern. This information iscollected by observational methods. Example: Auditing the provisional stores andcollecting data on inventories recorded by copying information from store records.

Pantry Audits : This method is used to estimate the consumption of the basket of thegoods at the consumer level. Here the researcher collects the inventory of types,quantities and prices of commodities consumed. Thus pantry audit data are recordedfrom the consumption of consumer's pantry. An important limitation of pantry audit isthat, sometimes the audit data alone may not be sufficient to identify the consumer'spreferences.

Consumer Panels : An extension of Pantry Audit approach on regular basis is knownas Consumer Panels. A set of consumers are arranged to come to an understanding tomaintain a daily records of their consumption and the same is made available toresearcher on demand. In other words Consumer Panel is a sample of consumersinterviewed repeatedly over a period of time.

Field works : To collect the primary data any researcher or investigator may aredifferent methods wherein they go to door to door, use telephone to collect data.

SUMMARY

Since there are various methods of data collection, the researcher must select theappropriate data. Hence, the following factors to be kept in mind by the researcher:

1. Nature, Scope and Object of the Enquiry

2. Availability of funds

3. Time factor

4. Precision required

KEY TERMS

· Primary data· Secondary data· Interview· Questionnaire· Schedule· Observation· Survey· Warranty cards· Pantry Audits· Distributor Audits· Consumer Panels

QUESTIONS

1. Describe the different data sources, explaining their advantages and disadvantages.

2. What is bias and how it can be reduced during interviews?

3. "Every data collection method has it own built in biases. Therefore resorting to multimethods of data collection is only going to compound the biases". How would youevaluate the statement?

4. Discuss the role technology in data collection.

5. What is your view on using the warranty cards and Distributor audits in datacollection?

6. Differentiate the questionnaire and Interview schedules to decide the best one.

7. Discuss the main purposes for which Survey methods are used.

- End of Chapter -

LESSON – 10

SAMPLING METHODS

OBJECTIVES

· To define the terms Sampling, Sample, Population· To describe the various sampling designs

· To discuss the importance of Confidence and Precision· To identify and use the appropriate sampling designs for different research

purposes

STRUCTURE

· Universe/population· Sampling· Sampling techniques· Importance of sample design and sample size

INTRODUCTION

Sampling Methods is a process of selecting sufficient number of elements from thepopulation. This is also understood as the process of obtaining information about entirepopulation by examining only a part of it. So sample can be defined as a subset of thepopulation. In other words, some, but not all elements of the population would form thesample.

Basically sampling helps a researcher in variety of ways as follows:

· It saves time and money. A sample study usually is less expensive than apopulation survey.

· It also helps the researcher to obtain the accurate results.· Sampling is only way when the population is very large in size.· It enables to estimate the sampling error so; this assists in obtaining information

and in convening the characteristics of population.

To understand the sampling process, the researcher also should understand thefollowing terms:

1. Universe / Population

In any of the research, the interest of the researcher is mainly in studying the variouscharacteristics relating to items or individuals belonging to a particular group. Thisgroup of individuals under study is known as the population or universe.

2. Sampling

A finite subset-selected from a population with the objective of investigating itsproperties is called a "sample".

The number of units in the sample is known as the 'sample size'. This is the importantrole of any research which enables to draw conclusions about characteristics of thepopulation.

3. Parameter & Statistics

The statistical constants used for further analysis of Data collected such as Mean (μ),Variance (σ2), Skewness (β1), Kurtosis (β2), Correlation (γ) can be computed for thesample drawn from the population.

Sampling is the important part of any research before data collection. So the samplingprocess should be done in a careful way to obtain the exact samples and sample size ofthe population on which the research is to be done.

Example: A researcher who would like to study the customer satisfaction for a healthdrink namely Horlicks should identify the population who are consuming Horlicks. Ifthe consumers are varying in age, genders all over the state or country, he should be ableto decide to particular consumers are going to be focused. Again, if the number is moreto survey he has to decide on how many individuals he targets for his study.

Hence the effecting sampling process should have the following steps:

Define the population

(Elements, units, extent, and time)

↓

Specify the sample frame

(The mean of representing the elements of population map, city directory)

↓

Specifying the sampling unit

(Sampling unit containing more population elements)

↓

Specifying the sampling method

(The method by which sampling units are to be selected)

↓

Determine the sample size

(The no. of elements of the population to decided)

↓

Sampling plan

(Procedure for selected sampling unit)

↓

Select the sample

(The effective and field work revision for section of samples)

Hence a sample design is a definite plan for obtaining a sample from a given population.So whenever samples have to be decided for the study, the following can be considered:

- Outline the universe

- Define a sampling unit

- Sampling frame

- Size of the sample

Sampling Techniques

Sampling techniques can be divided into two types:

1. Probability or representative sampling

a. Simple random sampling

b. Stratified random sampling

c. Systematic sampling

d. Cluster sampling

e. Multistage sampling

2. Non probability or judgmental sampling

a. Quota sampling

b. Purposive sampling

Other methods

· Snow ball sampling

· Spatial sampling· Saturation sampling

1. Probability Sampling

This is a scientific technique of drawing samples form the population according to somelaws of change according to which each unit in the universe has some definite pre-assigned probability of being selected in the sample.

Simple Random Sampling

In this technique, sample is drawn in such a way that every elements or unit in thepopulation has an equal and independent chance of being included in the sample.

The unit selected in any draw from the population is not preplanned in populationbefore making the next draw is known as simple random sampling without replacement.

If the unit is replaced back before making the next draw the sampling plan is called assimple random sampling with replacement.

Stratified Random Sampling

When the population is heterogeneous with respect to the variable or characteristicsunder the study this sampling method is used. Stratification means division intohomogenous layers or groups. Stratified random sampling involves stratifying the givenpopulation into a number of sub-groups or sub-population known as strata.

The characteristics of stratified samples are as follows:

· The units within each stratum are as homogenous as possible.· The differences between various strata are as marked as possible.· Each and every unit in the population belongs to one and only one stratum.

The population can be stratified according to geographical, sociological or economiccharacteristics. Some of the commonly used stratifying factors are age, sex, income,occupation, education level, geographic area, economic status etc. To decide on the no.of samples or items drawn from the different strata, will be wept proportional to thesizes of the strata.

Example: If pi represents the proportion of the population included in stratum 'i', andn represents the total sample size, then the number of elements selected from stratum iis (n - pi)

Example: Suppose we need a sample size of n = 30 to be drawn from a population ofsize N= 6000 which is divided into three strata of sizes N1 = 3000, N2 = 1800, N3 =1200.

Total population = 3000+1800+1200 = 6000

Hence using the proportional allocation, the sample size for different strata are 15, 9,and 6, which are proportionate to the strata sizes of 3000, 1800, and 1200.

Systematic Sampling

This sampling is a slight variation of simple random sampling in which only the firstsample unit is selected at random while remaining units are selected automatically in adefinite sequence at equal spacing from one another. This kind of sampling isrecommended only when if a complete and up to date list of sampling units is availableand the units are arranged in a systematic order as alphabetical, chronological,geographical etc.

Systematic sampling can be taken as an improvement over a simple random samplingsince it spreads more evenly over the entire population. This method is one of the easierand less costly methods of sampling and can be conveniently used in case of largepopulation.

Cluster Sampling

If the total area of interest happens to be a big one, a convenient way in which a samplecan be taken is to divide the area into a number of smaller non-overlapping areas andthen to randomly select a number of these smaller areas.

In cluster sampling, the total population is divided into a number of relatively small subdivisions which are themselves clusters of still smaller units and some of these clustersare randomly selected for inclusion in overall sample. Cluster sampling reduces the cost

by concentrating surveys in clusters. But this type of sampling is less accurate thanrandom sampling.

Multistage Sampling

It is a further development of the principle of cluster sampling. In case of investigatingthe working efficiency of nationalized banks in India, a sample of few banks may betaken for the purpose of investigation.

Here to select the banks as a first step, the main states in a country are selected from thestates from which the banks to be included for the study will be selected. This representsthe two stage sampling. Even further, from the district certain towns may be selected,from where the banks will be selected. This may represent three stages sampling.

Even thereafter, instead of taking census from all the banks in all the towns we haveselected, once again banks may be selected randomly for the survey. Hence the randomselection at all levels (various levels) is known as multistage random sampling design.

Sequential Sampling

This is one of the complex sampling designs. The ultimate size of sample in thistechnique is not fixed in advance but it is determined according to the mathematicaldecision rules on the basis of information yielded in the survey.

This method is adopted when sampling plan is accepted in context of Statistical QualityControl.

Example: When a lot is to be accepted or rejected on the basis of single sample, it isknown as single sampling; when the decision is to be taken on the basis of twosamples it is known as double sampling, and in case the decision is based on themore than two samples but the number of samples is certain and decided in advance,the sampling is known as multi sampling. In case when the number of samples ismore than two but it is neither certain nor decided in advance, this type of system isoften referred to as Sequential Sampling. So in case of Sequential Sampling, one cango on taking samples one after another as long as one desires to do so.

2. Non-probability Sampling

Quota Sampling

This is stratified-cum-purposive or judgment sampling and thus enjoys the benefits ofboth. It aims at making the best use of stratification without incurring the high costsinvolved in probabilistic methods. There is considerable saving in time and money asthe simple units may be selected that they are close together. If carefully experienced byskilled and experienced investigators who are aware of the limitations of judgmentsampling and if proper controls are imposed on the investigators, this sampling methodmay give reliable results.

Purposive or Judgment Sampling

A desired number of sampling units are selected deliberately so that only importantitems representing the true characteristics of the population are included in the sample.A major disadvantage of this sampling is that it is highly subjective, since the selectionof the sample depends entirely on the personal convenience and beliefs.

Example: In the case of socio-economic survey on the standard of living from people inChennai, if the researcher wants to show that the standard has gone down, he mayinclude only individuals from the low income stratum of the society in the samples andexclude people from rich areas.

Other Forms of Sampling

Snow Ball Sampling : This method is used in the cases where information about unitsin the population is not available. If a researcher wants to study the problem of theweavers in a particular region, he may contact the weavers who are known to him. Fromthem, he may collect the addresses of other weavers in the various parts of the region heselected. From them again he may collect the information on other known weavers tohim. By repeating like this for several times, he will be able to identify and contact themajority of weavers from a selected region. He could then draw a sample from thisgroup. This method is useful only when individuals in the target group have contact withone another, and also willing to reveal the names of others in the group.

Spatial Sampling : Some populations are not static and moving from place to placebut staying at one place when an event is taking place. In such case the whole populationin a particular place is taken into the sampling and studied.

Example: The number of people living in Dubai may vary depending on many factors.

Saturation Sampling : Sometimes if all members of population is need to be studiedso as to get a picture of entire population. The sampling method that requires a study ofentire population is called Saturation Sampling. This technique is more familiar in Sociometric studies where in distorted results will be produced even if one person is left out.

Example: In case of analyzing the student's behavior of one particular class room, allthe students in the class room must be examined.

From the above discussion on sampling methods, normally one may resort to simplerandom sampling since biasness is generally eliminated in this type of sampling. At thesame time, purposive sampling is considered more appropriate when the universehappens to be small and a known characteristic of it is to be studied intensively. Insituations where random sampling is not possible then it is advisable to use necessarilya sampling design other than random sampling.

Determination of Sample size

Determination of appropriate sample size is crucial part of any business research. Thedecision on proper sample size tremendously requires the use of statistical theory. Whena business research report is been evaluated, the evaluation start with the question of'how big is the sample size?'

Having discussed various sampling designs it is important to focus the attention onSample Size. Suppose we select a sample size of 30 from the population of 3000 througha simple random sampling procedure, will we able to generalize the findings to thepopulation with confidence? So in this case what is the sample size that would berequired to carry out the research?

It is the known fact that larger the sample size, the more accurate the research is. In factthis is the fact based on the statistics. According to this fact, increasing the sample sizedecreases the width of the confidence interval at a given confidence level. When thestandard deviation of the population is unknown, a confidence interval is calculated byusing the formula:

Confidence Interval,

μ = X ± KSx

where,

Sx = S / Sqrt(n)

In sum, choosing the appropriate sampling plan is one of the important research designdecisions the researcher has to make. The choice of a specific design will depend broadlyon the goal of research, the characteristics of the population, and considerations of cost.

Issues of Precision and Confidence in determining Sample size

We now need to focus attention on the second aspect of the sampling design issue—thesample size. Suppose we select 30 people from a population of 3,000 through a simplerandom sampling procedure. Will we be able to generalize our findings to thepopulation with confidence? What is the sample size that would be required to makereasonably precise generalizations with confidence? What do precision and confidencemean?

A reliable and valid sample should enable us to generalize the findings from the sampleto the population under investigation. No sample statistic (X, for instance) is going to beexactly the same as the population parameter (Sx), no matter how sophisticated theprobability sampling design is. Remember that the very reason for a probability designis to increase the probability that the sample statistics will be as close as possible to thepopulation parameters.

Precision

Precision refers to how close our estimate is to the true population characteristic.Usually, we would estimate the population parameter to fall within a range, based on thesample estimate.

Example: From a study of a simple random sample of 50 of the total 300 employees ina workshop, we find that the average daily production rate per person is 50 pieces of aparticular product (X = 50). We might then (by doing certain calculations, as we shallsee later, be able to say that the true average daily production of the product (X) wouldlie anywhere between 40 and 60 for the population of employees in the workshop. Insaying this, we offer an interval estimate, within which we expect the true populationmean production to be (μ = 50 ± 10). The narrower this interval, the greater is theprecision. For instance, if we are able to estimate that the population mean would fallanywhere between 45 and 55 pieces of production (μ = 50 ± 5) rather than 40 and 60 (μ= 50 ± 10), then we would have more precision. That is, we would now estimate themean to lie within a narrower range, which in turn means that we estimate with greaterexactitude or precision.

Precision is a function of the range of variability in the sampling distribution of thesample mean. That is, if we take a number of different samples from a population, andtake the mean of each of these, we will usually find that they are all different, arenormally distributed, and have a dispersion associated with them Even if we take onlyone sample of 30 subjects from the population, we will still be able to estimate thevariability of the sampling distribution of the sample mean. This variability is called thestandard error, denoted by 'S'. The standard error is calculated by the following formula:

Sx = S / Srqt(n)

where,

S = Standard deviation of the sample

n = Sample size

Sx = Standard error or the extent of precision offered by the sample.

In sum, the closer we want our sample results to reflect the population characteristics,the greater will be the precision we would aim at. The greater the precision required, thelarger is the sample size needed, especially when the variability in the population itself islarge.

Confidence

Whereas precision denotes how close we estimate the population parameter based onthe sample statistic, confidence denotes how certain we are that our estimates will reallyhold true for the population. In the previous example of production rate, we know weare more .precise when we estimate the true mean production (μ) to fall somewherebetween 45 and 55 pieces, than somewhere between 40 and 60.

In essence confidence reflects the level of certainty with which we can state that ourestimates of the population parameters, based on our sample statistics will hold true.The level of confidence can range from 0 to 100%. A 95% confidence is theconventionally accepted level for most business research, most commonly expressed bydenoting the significance level as p = .05. In other words, we say that at least 95 timesout of 100, our estimate will reflect the true population characteristic.

In sum, the sample size n, is a function of

1. The variability in the population

2. Precision or accuracy needed

3. Confidence level desired

4. Type of sampling plan used, for example, sample random sampling versus stratifiedrandom sampling

It thus becomes necessary for researchers to consider at least four points while makingdecisions on the sample size needed to do the research:

(1) Much precision is really needed in estimating the population characteristics interest,that is, what is the margin of allowable error?

(2) How much confidence is really needed, i.e. how much chance can we take of makingerrors in estimating the population parameters?

(3) To what extent is there variability in the population on the characteristicsinvestigated?

(4) What is the cost-benefit analysis of increasing the sample size?

Determining the Sample Size

Now that we are aware of the fact that the sample size is governed by the extent ofprecision and confidence desired, how do we determine the sample, retired for ourresearch? The procedure can be illustrated through an example:

Suppose a manager wants to be 95% confident that the withdrawals in a bank will bewithin a confidence interval of ±$500. Example of a simple of clients indicates that theaverage withdrawals made by them have a standard deviation of $3,500. What would bethe sample size needed in this case?

We noted earlier that the population mean can be estimated by using the formula:

μ = X ± KSx

Given, S = 3500. Since the confidence level needed here is 95%, the applicable K value is1.96 (t-table). The interval estimate of ±$500 will have to encompass a dispersion of(1.96 x standard error). That is,

The sample size needed in the above is 188. Let us say that this bank has the totalclientele of only 185. This means we cannot sample 188 clients. We can, in this case,apply the correction formula and see what sample size would be needed to have thesame level of precision and confidence given the fact that we have a total of only 185clients. The correction formula is as follows:

where,

N = total number of elements in the population = 185

n = sample size to be estimated = ?

Sx = Standard error of estimate of the mean = 255.10

S = Standard deviation of the sample mean = 3500

Applying the correlation formula,

we find that

255.10 = 3500 × √n × √185-n/184

the value of n to be 94.

We would now sample 94 of the total 185 clients.

To understand the impact of precision and/or confidence on the sample size, let us trychanging the confidence level required in the bank withdrawal exercise which needed asample size of 188 for a confidence level of 95%. Let us say that the bank manager nowwants to be 99% sure that the expected monthly withdrawals will be within the intervalof ±$500. What will be the sample size now needed?

The sample has now to be increased 1.73 times (from 188 to 325) to increase theconfidence level from 95% to 99%.It is hence a good idea to think through how muchprecision and confidence one really needs, before determining the sample size for theresearch project.

So far we have discussed sample size in the context of precision and confidence withrespect to one variable only. However, in research, the theoretical framework hasseveral variables of interest, and the question arises how one should come up with asample size when all the factors are taken into account.

Krejcie and Morgan (1970) greatly simplified size decision by providing a table thatensures a good decision model. The Table provides that generalized scientific guidelinefor sample size decisions. The interested student is advised to read Krejcie and Morgan(1970) as well as Cohen (1969) for decisions on sample size.

Importance of Sampling Design and Sample Size

It is now possible to see how both sampling design and the sample size are important toestablish the representativeness of the sample for generality. If the appropriatesampling design is not used, a large sample size will not, in itself, allow the findings tobe generalized to the population. Likewise, unless the sample size is adequate for thedesired level of precision and confidence, no sampling design, however sophisticated,can be useful to the researcher in meeting the objectives of the study.

Hence, sampling decisions should consider both the sampling design and the samplesize. Too large a sample size, however (say, over 500) could also become a problem in as

much as we would be prone to committing Type II errors. Hence, neither too large nortoo small sample sizes help research projects.

Roscoe (1975) proposes the following rules of thumb for determiningsample size:

1. Sample sizes larger than 30 and less than 500 are appropriate for most research.

2. Where samples are to be broken into sub samples; (male/females, juniors/ seniors,etc.), a minimum sample size of 30 for each category is necessary.

3. In multivariate research (including multiple regression analyses), the sample sizeshould be several times (preferably 10 times or more) as large as the number ofvariables in the study.

4. For simple experimental research with tight experimental controls (matched pairs,etc.), successful research is possible with samples as small as 10 to 20 in size.

KEY TERMS

1. "What is Sample Design"? What all are the points to be considered to develop asample design?

2. Explain the various sampling methods under probability sampling.

3. Discuss the non probability sampling methods.

4. What are the importance of sample size and sampling design?

5. Discuss the other sampling methods.

6. Explain why cluster sampling is a probability sampling design.

7. What are the advantages and disadvantages of cluster sampling?

8. Explain what precision and confidence are and how they influence sample size.

9. The use of a convenience sample used in organizational research is correct because allmembers share the same organizational stimuli and go through almost the same kindsof experience in their organizational life. Comment.

10. Use of a sample of 5,000 is not necessarily better than one of 500. How would youreact to this, statement?

11. Non-probability sampling designs ought to be preferred to probability samplingdesigns in some cases. Explain with an example

- End of Chapter -

LESSON – 11

THE NATURE OF FIELD WORK

OBJECTIVES

· To recognize that field work can be performed by many different parties.· To understand the importance of training for new interviewers· To understand the principle tactics of asking questions

STRUCTURE

· Interviewing· Training for interviewing· The major principle for asking questions· Probing· Recording the response

INTRODUCTION

A personal interviewer administering a questionnaire door to door, a telephoneinterviewer calling from a central location, an observer counting pedestrians in ashopping mall, and others involved in the collection of data and the supervision of thatprocess are all Field Workers in the field. The activities of the field workers may vary innature. This lesson would help to understand the interview methods in data collectionprocess of the research and field work management.

Who conducts the field work?

Data collection is rarely carried out by the person who designs the research project.However, the data collecting stage is crucial, because the research project is no betterthan the data collected in the field. Therefore, it is important that the researchadministrator select capable people who may be entrusted to collect the data. An ironyof business research is that highly educated and trained individuals design the research,but the people who collect the data typically have little research training or experience.Knowing the vital importance of data collected in the field, research administratorsmust concentrate on carefully selecting field workers.

INTERVIEWING

Interviewing process is establishing rapport with the, respondent Interviewer bias mayenter in if the field worker's clothing or physical appearance is unattractive or unusual.Suppose that a male interviewer, wearing a dirty T-shirt, interviews subjects in anupper-income neighborhood. Respondents may consider the interviewer slovenly andbe less cooperative than they would be with a person dressed more appropriately.

Interviewers and other fieldworkers are generally paid an hourly rate or a per-interviewfee. Often interviewers are part-time workers, housewives, graduate students, secondaryschool teachers from diverse backgrounds. Primary and secondary school teachers arean excellent source for temporary interviewers during the summer, especially when theyconduct interviews outside the school districts where they teach. Teachers' educationalbackgrounds and experiences with the public make them excellent candidates forfieldwork.

TRAINING FOR INTERVIEWERS

The objective of training is to ensure that the data collection instrument is administereduniformly by all field investigators. The goal of training sessions is to ensure that eachrespondent is provided with common information. If the data are collected in a uniformmanner from all respondents, the training session will have been a success. Afterpersonnel are recruited and selected, they must be trained.

Example: A woman who has just sent her youngest child off to first grade is hired by aninterviewing firm. She has decided to become a working mother by becoming aprofessional interviewer. The training that she will receive after being selected by acompany may vary from virtually no training to a 3-day program if she is selected by oneof the larger survey research agencies. Almost always there will be a briefing session onthe particular project. Typically, the recruits will record answers on a practicequestionnaire during a simulated training interview.

More extensive training programs are likely to cover the following topics:

1. How to make initial contact with the respondent and secure the interview

2. How to ask survey questions

3. How to probe

4. How to record responses

5. How to terminate the interview

Making Initial Contact and Securing the Interview

Interviewers are trained to make appropriate opening remarks that will convince theperson that his or her cooperation is important.

Example: "Good afternoon, my name is _____ and I'm from a national surveyresearch company. We are conducting a survey concerning. I would like to get a few ofyour ideas".

Much fieldwork is conducted by research suppliers who specialize in data collection.When a second party is employed, the job of the study designed by the parent firm is notonly to hire a research supplier but also to establish supervisory controls over the fieldservice.

In some cases a third party is employed. For example, a firm may contact a surveyresearch firm, which in turn subcontracts the fieldwork to a field se vice. Under thesecircumstances it is still desirable to know the problems that might occur in the field andthe managerial practices that can minimize them.

Asking the Questions

The purpose of the interview is, of course, to have the interviewer ask questions andrecord the respondent's answers. Training in the art of stating questions can beextremely beneficial, because interviewer bias can be a source of considerable error insurvey research.

There are five major principles for asking questions:

i. Ask the questions exactly as they are worded in the questionnaire.

ii. Read each question very slowly.

iii. Ask the questions in the order in which they are presented in the questionnaire.

iv. Ask every question specified in the questionnaire.

v. Repeat questions those are misunderstood or misinterpreted.

Although interviewers are generally trained in these procedures, when working in thefield many interviewers do not follow them exactly. Inexperienced interviewers may notunderstand the importance of strict adherence to the instructions. Even professionalinterviewers take shortcuts when the task becomes monotonous. Interviewers mayshorten questions or rephrase unconsciously when they rely on their memory of thequestion rather than reading the question as it is worded. Even the slightest change inwording can distort the meaning of the question and cause some bias to enter into astudy. By reading the question, the interviewer may be reminded to concentrate onavoiding slight variations in tone of voice on particular words phases in the question.

PROBING

General training of interviewers should include instructions on how to probe whenrespondents give no answer, incomplete answers, or answers that require clarification.

Probing may be needed for two types of situations. First, it is necessary when therespondent must be motivated to enlarge on, clarify or explain his or her answer. It isthe interviewer's job to probe for complete, unambiguous answers. The interviewer mustencourage the respondent to clarify or expand on answers by providing a stimulus thatwill not suggest the interviewer's own ideas or attitudes. The ability to probe withneutral stimuli is the mark of an experienced interviewer. Second, probing may benecessary in situations in which the respondent begins to ramble or lose track of thequestion. In such cases the respondent must be led to focus on the specific content ofthe interview and to avoid irrelevant and unnecessary information.

The interviewer has several possible probing tactics to choose from,depending on the situation:

i. Repetition of the question: The respondent who remains completely silent maynot have understood the question or may not have decided how to answer it. Mererepetition may encourage the respondent to answer in such cases. For example, if thequestion is "What is there that you do not like about your supervisor?" and therespondent does not answer, the interviewer may probe: "Just to check; is thereanything you do not like about your supervisor?"

ii. An expectant pause: If the interviewer believes the respondent has more to say,the "silent probe" accompanied by an expectant look, may motivate the respondent togather his or her thoughts and give a complete response Of course, the interviewer mustbe sensitive to the respondent so that the silent probe does not become an embarrassedsilence.

iii. Repetition of the Respondent's Reply: Sometimes the interviewer may repeatthe verbatim of the respondent. This may help the respondent to expand the answer.

RECORDING THE RESPONSES

The analyst who fails to instruct fieldworkers in the techniques of recording answers forone study rarely forgets to do so in the second study. Although the concept of recordingan answer seems extremely simple, mistakes can be made in the recording phase of theresearch. All fieldworkers should use the same mechanics of recording.

Example: It may appear insignificant to the interviewer whether she uses a pen orpencil, but to the editor who must erase and rewrite illegible words, using a pencil isextremely important.

The rules for recording responses to closed questionnaires vary with the specificquestionnaire. The general rule, however, is to place a check in the box that correctlyreflects the respondent's answer. All too often interviewers don't bother recording theanswer to a filter question because they believe that the subsequent answer will makethe answer to the filter question obvious. However, editors and coders do not know howthe respondent actually answered a question.

The general instruction for recording answers to open-ended-response questions is torecord the answer verbatim, a task that is difficult for most people. Inexperiencedinterviewers should be given the opportunity to practice

The Interviewer's Manual of the Survey Research Center provides the instructions onthe recording of interviews. Some of its suggestions:

· Recording answers to open-ended-response questions follow· Record the responses during the interview· Use the respondent's own words· Do not summarize or paraphrase the respondent's answer· Include everything that pertains to the question objectives· Include all of your probes

The basics of effective Interviewing

Interviewing is a skilled occupation; not everyone can do it, and even few can do itextremely well. A good interviewer observes the following principles:

1. Have integrity and be honest.

2. Have patience and tact.

3. Pay attention to accuracy and detail.

4. Exhibit the real enquiry at hand, but keep your own opinions to yourself.

5. Be a good listener.

6. Keep the inquiry and respondent's responses confidential. Respect other's rights

Terminating the Interview

The final aspect of training deals with instructing the interviewers on how to close theinterview. Fieldworkers should not close the interview before pertinent information hasbeen secured. The interviewer whose departure hasty will not be able to record thosespontaneous comments responds sometimes offer after all formal questions have beenasked. Avoiding hasty departures is also a matter of courtesy.

Fieldworkers should also answer to the best of their ability any quest the respondent,concerning the nature and purpose of the study. Beat the fieldworker may be required tore-interview the respondent at some his time, he or she should leave the respondentwith a positive feeling about having cooperated in a worthwhile undertaking. It isextremely important thank the respondent for his or her cooperation.

FIELDWORK MANAGEMENT

Managers of the field operation select, train, supervise, and control fieldworkers. Ourdiscussion of fieldwork principles mentioned selection and training. This sectioninvestigates the tasks of the fieldwork manager in greater detail.

Briefing Session for Experienced Interviewers

After interviewers have been trained in fundamentals, and even when they have becomeexperienced, it is always necessary to inform workers about the individual project. Bothexperienced and inexperienced fieldworkers must be instructed on the background ofthe sponsoring organization, sampling techniques, asking questions, callbackprocedures, and other matters specific to the project.

If there are special instructions - for example, about using show cards or videoequipment or about restricted interviewing times-these should also be covered duringthe briefing session. Instructions for handling certain key questions are alwaysimportant. For example, the following fieldworker instructions appeared in a survey ofinstitutional investors who make buy-and sell decisions about stocks for banks, pensionfunds, and the like.

A briefing session for experienced interviewers might go like, All interviewers report tothe central office, where the background of the firm and the general aims of the studyare briefly explained. Interviewers are not provided with too much information aboutthe purpose of the study, thus ensuring that they will not transmit any preconceivednotions to respondents. For example, in a survey about the banks in a community, theinterviewers would be told that the research is a banking study, but not the name of thesponsoring bank. To train the interviewers about the questionnaire, a field supervisorconducts an interview with another field supervisor who acts as a respondent. Thetrainees observe the interviewing process, after which they each interview and recordthe responses of another field supervisor. Additional instructions are given to thetrainees after the practice interview.

Training to Avoid Procedural Errors in Sample Selection

The briefing session also covers the sampling procedure. A number of research projectsallow the interviewer to be at least partially responsible for selection of the sample.When the fieldworker has some discretion in the selection of respondents, the potentialfor selection bias exists. This is obvious in the case of quota sampling, but less obviousin other cases.

Example: In probability sampling where every nth house is selected, the fieldworkeruses his or her discretion in identifying housing units. Avoiding selection error may notbe as simple as it sounds.

Example: In an older, exclusive neighborhood, a mansion's coach house or servant'squarters may have been converted into an apartment that should be identified as ahousing unit. This type of dwelling and other unusual housing units (apartments withalley entrances only, lake cottages, rooming houses) may be overlooked, giving rise to

selection error. Errors may also occur in the selection of random digit dialing samples.Considerable effort should be expended in training and supervisory control to minimizethese errors.

The activities involved in collecting data in the field may be performed by theorganization needing information, by research suppliers, or by third party field serviceorganizations. Proper execution of fieldwork is essential for producing research resultswithout substantial error.

Proper control of fieldwork begins with interviewer selection. Fieldworkers shouldgenerally be healthy, outgoing, and well groomed. New fieldworkers must be trained inopening the interview, asking the questions, probing for additional information,recording the responses, and terminating the interview. Experienced fieldworkers arebriefed for each new project so that they are familiar with its specific requirements. Aparticular concern of the briefing session is reminding fieldworkers to adhere closely tothe prescribed sampling procedures.

Careful supervision of fieldworkers is also necessary. Supervisors gather and editquestionnaires each day. They check to see that field procedures are properly followedand that interviews are on schedule. They also check to be sure that the proper samplingunits are used and that the proper people are responding in the study. Finally,supervisors check for interviewer cheating and verify a portion of the interviews by re-interviewing a certain percentage of each fieldworker's respondents.

SUMMARY

This paper outlined the importance of training for new interviewers. In this chapter fivemajor principles for asking questions have been dealt in detail.

KEY TERMS

· Field worker· Probing· Field interviewing· Briefing session· Training Interview· Reinterviewing questions

QUESTIONS

1. What qualities should a field worker possess?

2. What is the proper method of asking questions?

3. When should an interviewer probe? Give examples of how probing should be done?

4. How should an Interviewer terminate the interview?

5. What are the qualities of the interviewer that make him more effective?

REFERENCES

1. Ramanuj Majumdar, Marketing Research, Wiley Eastern Limited New Delhi (1991)

2. Cochran, W.G., Sampling Techniques, 2nd ed. New York: John Wiley and Sons.

3. Chaturvedi, J.C., Mathematical Statistics, Agra: Nok Jhonk Karyalaya, 1953.

- End of Chapter -

LESSON – 12

SOURCES OF DATA

Sources of data - primary - secondary data - Questionnaire design: attitudemeasurement techniques - motivational research techniques - selection appropriatestatistical techniques - correlation - research.

OBJECTIVES

· To explain the difference between secondary and primary data· To discuss the advantages and disadvantages of secondary data· To learn the nature of secondary data· To understand the evaluation of secondary data sources· To learn the sources of secondary data

STRUCTURE

· Value of secondary data· Disadvantage of secondary data· Nature and scope of secondary data· Sources of secondary data

INTRODUCTION

The availability of data source is very much needed to solve the problem and there aremany ways by which the data is collected. The task of data collection begins after aresearch problem has been defined and research designed is prepared. Thus the data tobe collected can be classified as being either secondary or primary. The determination ofdata source is based on three fundamental dimensions as given below:

1. The extent of data already exist in some type,

2. The degree to which the data has been interpreted by someone, and

3. The extent to which the researcher or decision maker understands the reasons andwhy the data was collected and researched.

Primary Data is the data gathered and assembled specifically for the project at hand. Itis "finished" raw data, and has yet to receive any type of meaningful interpretation. Theprimary data is fresh, and since it is collected for the first time, it happens to be originalin character. On the other hand, Secondary Data is that which has already been collectedby someone else and also passed through statistical process and interpretation.Secondary data is historical data structure of variables previously collected andassembled for some research problem other than the current situation.

The sources of primary data tend to be the output of conducting some type ofexploration, descriptive or casual research that employs surveys, experiments and / orobservation as technique of collecting the needed data. The greater insights underlyingprimary data will be discussed in the chapter "methods of data collection". The pros &cons of primary data also discussed with reference to various techniques involved in theprocess.

The source of secondary data can be found inside a company at public libraries, anduniversities, on World Wide Web (www) sites or purchased from a firm specializing inproviding secondary information. Here, evaluation and source of data are discussed.

THE VALUE / ADVANTAGES OF SECONDARY DATA

More and more companies are interested in using the existing data as a major tool in themanagement decisions. As more and more such data become available, many companiesare realizing that they can be used to make sound decisions. Data of this nature aremore readily available, often more highly valid and usually less expensive to secure thanprimary data.

"Nowhere in science do we start from scratch" - this quote explains the value ofsecondary data. Researchers are able to build on the past research - a body of businessknowledge. The researchers use other's experience and data when it is available assecondary data. The primary advantage of secondary data is that obtaining data isalmost always less expensive and in addition the data can usually be obtained rapidly.The major advantage and disadvantages are discussed below.

Advantages of Secondary Data are:

1. It is more economical as the cost of collecting original data is saved. In the collectionof primary data, a good deal of effort is required which includes preparation of datacollection forms, designing and printing of forms, persons appointed to collect data in

turn involves travel plan need to verify and finally data to be tabulated. All these needlarge funds which can be utilized elsewhere if secondary data can serve the purpose.

2. Another advantage is that the use of secondary data saves much of the time of theresearcher. This also leads to prompt completion of research project.

3. Secondary data are helpful not only because it is useful but the familiarity with thedata indicates deficiencies and gaps. As a result, the researcher can make the primarydata collection more specific and more relevant to the study.

4. It also helps in gaining new insights to the problem, then can be used to fine tune theresearch hypothesis and objectives.

5. Finally, secondary data can be used as a basis of comparison with primary data thathas been collected for this study.

DISADVANTAGES OF SECONDARY DATA

An inherent disadvantage of secondary data is that it is not designed specifically to meetthe researcher's needs. Secondary data quickly becomes outdated in our rapidlychanging environments. Since the purpose of the most of the studies is to predict thefuture, the secondary data must be timely. Hence the most common problems withsecondary data are:

1. Outdated information

2. Variation in definition of terms or classifications. The unit of measurement may causeproblems if they are not identical to the researcher's needs. Even though original unitswere comparable, the aggregated or adjusted units of measurements are not suitable forthe present study. When the data are reported in a format that does not exactly meet theresearchers needs, the data conversion may be necessary.

3. Another disadvantage of secondary data is that the user has to control over theiraccuracy even though it is timely & pertinent, they may be inaccurate.

THE NATURE AND SCOPE OF SECONDARY DATA

Focusing on the particular business or management problem, the researcher needs todetermine whether useful information already exists, of exists how relevant theinformation. Since existing information are more widespread than one might expect.The secondary data exists in three forms:

1. Internal secondary data: The data collected by the individual company for somepurpose and reported periodically. This is also called as primary sources. The primarysources are original work of research or raw data without interpretation orpronouncements that represent an official opinion or position - Memos, completeinterviews, speeches, laws, regulations, court decisions, standards, and most

government data, including census, economic and labor data. Primary sources arealways the most authoritative because the information is not filtered. It also includesinventory records, personnel records, process charts and similar data.

2. External secondary data: It consists of data collected by outside agencies such asgovernment, trade associations of periodicals. This is called as secondary sources.Encyclopedia, text books, handbooks, magazine and newspaper articles and most newscrafts are considered to secondary sources. Indeed all reference materials fall into thiscategory.

3. Computerized data sources: This includes internal and external data usuallycollected by specific companies with online information sources. This can be called asterritory sources. These are represented by indexes, bibliography and other finding aids,e.g., internet search engines.

Evaluation of secondary data sources

The emphasis on secondary data will increase if an attempt is made to establish a set ofprocedures to evaluate the secondary data regarding the quality of information obtainedvia secondary data sources. Specifically, if secondary data are to be used to assist in thedecision process, then they should be assessed according to the following principles.

1. Purpose: Since most secondary data are collected for purpose other than the one athand, the data must be carefully evaluated on how they relate to the current researchobjectives. Many times the original collection of data is not consistent with theparticular research study. These inconsistencies usually result from the methods andunits of measurement.

2. Accuracy: When observing secondary data researchers need to keep in mind whatwas actually measured. For example, if the actual purchases in a test market weremeasured, did they measure the first-time trial purchases or repeat purchases?Researchers must also asses the generality of the data.

3. Questions like i) was the data collected from certain groups only or randomly? ii)was the measure developed properly? iii) was the data presented as the total ofresponses from all respondents or were they categorized by age, sex or socio economicstatus?

4. In addition to the above dimensions, researchers must assess when the data werecollected. This factor not only damages the accuracy of the data but also may be uselessfor interpretation. Researchers also must keep in mind that the flaws in the researchdesign and methods will alter the current research in process.

5. Consistency: When evaluating any source of secondary data, a good strategy is toseek out multiple sources of the same data to assure consistency. For example, whenevaluating the economic characteristics of a foreign market, a researcher may try to

gather the same information from government sources, private business publicationsand specially import or export trade publications.

6. Credibility: Researcher should always question the credibility of the secondary datasource. Technical competence, service quality, reputation, and tracing and expertise ofpersonnel representing the organization are some measures of credibility.

7. Methodology: The quality of secondary data is only as good as the methodologyemployed to gather them. Flaws in methodological procedures could produce resultsthat are invalid, unreliable or not generalizable beyond the study itself. Therefore,researchers must evaluate the size and description of the sample, the response date, thequestionnaire, and the overall procedure for collecting the data (telephone, mail, orpersonal interview).

8. Bias: Researchers must try to determine the underlying motivation or hiddenagenda, if any, behind the secondary data. It is not uncommon to find many secondarydata sources published to advance the interest of commercial, political or other intersectgroups. Researchers should try to determine if the organization reporting the report ismotivated by certain purpose.

SOURCES OF SECONDARY DATA

A. Internal sources

Generally, internal data consists of sales or cost information. Data of this kind is foundin internal accounting or financial records. The two most useful sources of informationare sales invoices and accounts receivable reports; quarterly sales reports and salesactivity reports are also useful.

The major sources of internal secondary data are given below:

1. Sales invoices

2. Accounts receivable reports

3. Quality sales reports

4. Sales activity reports

5. Other types

a. customer letters

b. Customer comment cards

c. Mail order forms

d. Credit applications

e. Cash register receipts

f. Sales person expense reports

g. Employee exit interviews

h. Warranty cards

i. Post marketing research studies.

B. External Sources

When undertaking the search for secondary data researchers must remember that thenumbers of resources are extremely large. The researcher needs to connect the sourcesby common theme.

The key variables most often sought by the researchers are given below:

1. Demographic dimensions

2. Employment characteristics

3. Economic characteristics

4. Competitive characteristics

5. Supply characteristics

6. Regulations characteristics

7. International market characteristics

The external secondary data do not originate in the firm and are obtained from outsidesources. It may be noted that secondary data can be collected from the originatingsources or from secondary sources. For example, the office of economic advisor, GOI isthe originating source for wholesale prices. In contrast a publication such as RBIbulletin on wholesale price is a secondary source.

These data may be available through Government publications, non-governmentalpublications or syndicated services. Some examples are given below:

Government publications

1. Census by Registrar General of India

2. National Income by Central Statistical Organization also statistical abstract, annualsurvey of industries.

3. Foreign trade by Director General of Commercial Intelligence.

4. Wholesale price index by Office of Economic Advisor

5. Economic Survey - Dept of Economic Affairs.

6. RBI Bulletin - RBI

7. Agricultural Situation in India - Ministry of Agriculture

8. Indian Labor Year Book - Labor Bureau

9. National Sample Survey – Ministry of Planning

Non- government publications

Besides official agencies, there are number of private organizations which bring outstatistics in one form or another on a periodical basis of course industry and tradeassociations are important like:

1. Indian Cotton Mills Federation or Confederation of Indian Textile Industry - abouttextile industry.

2. Bombay Mill Owners Association - statistics of workers of mills.

3. Bombay Stock Exchange - on financial accounts & ratios.

4. Coffee Board - coffee statistics

5. Coir Board - coir & coir goods

6. Rubber Board - Rubber statistics

7. Federation of Indian Chambers of Commerce & Industry (FICCI)

Syndicated services

Syndicated services are provided by certain organization which collect and tabulateinformation on continuous basis. Reports based on marketing information are sentperiodically to subscribers. A number of research agencies offer customized researchservices to their clients like consumer research, advertising research etc.

Publication by international organizations

There are several International organizations that publish statistics in their respectiveareas.

SUMMARY

In this chapter the importance of secondary data has been outlined. Disadvantage ofsecondary data have been dealt in detail in this chapter. Sources of secondary data havebeen outlined in this chapter.

KEY TERMS

· Primary data· Secondary data· Advantages and disadvantages· Evaluation of secondary data· Sources of secondary data· Governmental publications· Syndicated services

QUESTIONS

1. Discuss the difference between primary and secondary data.

2. Explain the advantages and disadvantages of secondary data.

3. Write short notes on nature and scope of secondary data.

4. How will you evaluate the secondary data sources?

5. Discuss the internal and external sources of secondary data.

- End of Chapter -

LESSON - 13

QUESTIONNAIRE DESIGN

OBJECTIVES

· To recognize the importance and relevance of questionnaire design· To recognize that the type of information will influence the structure of

questionnaire· To understand the role data collection method in designing questionnaire· To understand how to plan and design without mistakes, and improve its layout· To know importance of pretesting.

STRUCTURE

· Questionnaire design· Phrasing question· Art of asking question· Layout of traditional questionnaires

Many experts in survey research believe that improving the wording of questions cancontribute far more to accuracy than can improvements in sampling. Experiments haveshown that the range of error due to vague questions or use of imprecise words may beas high as 20 or 30 percent. Consider the following example, which illustrates thecritical importance of selecting the word with the right meaning. The followingquestions differ only in the use of the words should, could, and might:

· Do you think anything should be done to make it easier for people to pay doctoror hospital bills?

· Do you think anything could be done to make it easier for people to pay doctor orhospital bills?

· Do you think anything might be done to make it easier for people to pay doctor orhospital bills?

The results from the matched samples: 82 percent replied something should be done, 77percent replied something could be done, and 63 percent replied something might bedone. Thus, a 19 percent difference occurred between the two extremes, should andmight. Ironically, this is the same percentage point error as in the Literary Digest Poll,which is a frequently cited example or error associated with sampling.

The chapter outlines procedure for questionnaire design and illustrates that a little bit ofresearch knowledge can be a dangerous thing.

A Survey Is Only As Good As the Questions It Asks

Each stage of the business research process is important because of its interdependencewith other stages of the process. However, a survey is only as good as the questions itasks. The importance of wording questions is easily overlooked, but questionnairedesign is one of the most critical stages in the survey research process.

"A good questionnaire appears as easy to compose as does a good poem. But it is usuallythe result of long, painstaking word". Business people who are inexperienced in businessresearch frequently believe that constructing a questionnaire in a matter of hours.Unfortunately, newcomers who naively believe that common sense and good grammarare all that are needed to construct a questionnaire generally learn that their hastyefforts are inadequate.

While common sense and good grammar are important in question writing, more isrequired in the art of questionnaire design. To assume that people will understand thequestions is a common error. People simply may not know what is being asked. Theymay be unaware of the product or topic interest, they may confuse the subject withsomething else, or the question may not mean the same thing to everyone interviewed.Respondents may refuse to answer personal questions. Further, properly wording thequestionnaire is crucial, as some problems may be minimized or avoided altogether if askilled researcher composes the questions.

QUESTIONNAIRE DESIGN: AN OVERVIEW OF THE MAJOR DECISIONS

Relevance and accuracy are the two basic criteria a questionnaire must meet if it is toachieve the researcher's purpose. To achieve these ends, a researcher who systematicallyplans a questionnaire's design will be required to make several decisions - typically, butnot necessarily, in the order listed below:

1. What should be asked?

2. How should each question be phrased?

3. In what sequence should the questions be arranged?

4. What questionnaire layout will best serve the research objectives?

5. How should the questionnaire be pretested? Does the questionnaire need to berevised?

What Should Be Asked?

During the early stages of the research process, certain decisions will have been madethat will influence the questionnaire design. The preceding chapters stressed the need tohave a good problem definition and clear objectives for the study. The problemdefinition will indicate which type of information must be collected to answer themanager's questions; different types of questions may be better at obtaining certaintypes of information than others. Further, the communication mediums used for datacollection - telephone interview, personal interview, or self-administered survey willhave been determined. This decision is another forward linkage that influences thestructure and content of the questionnaire. The specific questions to be asked will be afunction of the pervious decisions later stages of the research process also have animportant impact o questionnaire wording. For example, determination of the questionsthat should be asked will be influenced by the requirements for data analysis. As thequestionnaire is being designed, the researcher should be thinking about the types ofstatistical analysis that will be conducted.

Questionnaire Relevancy

A questionnaire is relevant if no unnecessary information is collected and if theinformation that is needed to solve the business problem is obtained. Asking the wrongor an irrelevant question is a pitfall to be avoided. If the task is to pinpointcompensation problems, for example, questions asking for general information aboutmorale may be inappropriate. To ensure information relevancy, the researcher must bespecific about data needs, and there should be a rationale for each item of information.

After conducting surveys, many disappointed researchers have discovered that someimportant questions were omitted. Thus, when planning the questionnaire design, it isessential to think about possible omissions. Is information being collected on therelevant demographic and psychographic variables? Are there any questions that mightclarify the answers to other questions? Will the results of the study provide the solutionto the manager's problem?

Questionnaire Accuracy

Once the researcher has decided what should be asked, the criterion of accuracybecomes the primary concern. Accuracy means that the information is reliable and validwhile experienced researchers generally believe that one should use simple,understandable, unbiased, unambiguous, nonirritating words, no step-by-stepprocedure to ensure accuracy in question writing can be generalized across projects.Obtaining accurate answers from respondents is strongly influenced by the researcher'sability to design a questionnaire that facilitates recall and that will motivate therespondent to cooperate.

Respondent tend to be most cooperative when, the subjects of the research isinteresting. Also, if questions are not lengthy, difficult to answer, or ego threatening,there is higher probability of obtaining unbiased answers, question wording andsequence substantially influence accuracy. These topics are treated in subsequentsections of this chapter.

PHRASING QUESTIONS

There are many ways to phrase question, and many standard question formats havebeen developed in previous research studies. This section presents h classification ofquestion types and provides some helpful guidelines to researchers who must writequestions.

Open-Ended Response versus Fixed-Alternative Questions

Questions may be categorized as either of two basic types, according to the amount offreedom respondents are given in answering them. Response questions pose someproblem or topic and ask the respondent to answer in his or her own words. Forexample:

What things do you like most about your job?

What names of local banks can you think of offhand?

What comes to mind when you look at this advertisement?

Do you think that there are some ways in which life in the United States is gettingworse? How is that?

If the question is asked in a personal interview, the interviewer may probe for moreinformation by asking such questions as: Anything else? or Could you tell me moreabout your thinking on that? Open-ended response questions are free-answerquestions. They may be contrasted to the fixed-alternative question, sometimes called a"closed question", in which the respondent is given specific, limited-alternativeresponses and asked to choose the one closest to his or her own viewpoint. For example:

Did you work overtime or at more than one job last week?

Yes ____ No _____

Compared to ten years ago, would you say that the quality of most products made inJapan is higher, about the same, or not as good?

Higher ____ About the same _____ Not as good _____

Open-ended response questions are most beneficial when the researcher is conductingexploratory research, especially if the range of responses is not known. Open-endedquestions can be used to learn what words and phrases people spontaneously give to thefree-response questions. Respondents are free to answer with whatever is uppermost intheir thinking. By gaining free and uninhibited responses, a researcher may find someunanticipated reaction toward the topic. As the responses have the "flavor" of theconversational language that people use in talking about products or jobs, responses tothese questions may be a source for effective communication.

Open-ended response questions are especially valuable at the beginning of an interview.They are good first questions because they allow respondents up warm up to thequestioning process.

The cost of open-ended response questions is substantially greater than that of fixed-alternative questions, because the job of coding, editing and analyzing the data is quiteextensive. As each respondent's answer is somewhat unique, there is some difficulty incategorizing and summarizing the answers. The process requires an editor to go over asample of questions to classify the responses in to some sort of scheme, and then all theanswers are received and coded according to the classification scheme.

Another potential disadvantage of the open-ended response question is that interviewermay influence the responses. While most instructions state that the interviewer is torecord answers verbatim, rarely can even the best interviewer get every word spoken bythe respondent. There is a tendency for interviewer to take short-cuts in recordinganswers - but changing even a few of the respondents' words may substantially influencethe results. Thus, the final answer often is a combination of the respondent's and theinterviewer's ideas rather than the respondent's ideas alone.

The simple-dichotomy or dichotomous-alternative question requires therespondent to choose one of two alternatives. The answer can be a simple "yes" or "no"or a choice between "this" and "that". For example:

Did you make any long-distance calls last week?

Yes _____ No _____

Several types of questions provide the respondent with multiple-choice alternatives. Thedeterminant-choice questions require the respondent to choose one and only oneresponse from among several possible alternatives. For example:

Please give us some information about your flight. In which section of the aircraft didyou sit?

First Class _______ Business Class ______ Coach Class ______

The frequency-determination question is a determinant-choice question that asksfor an answer about general frequency of occurrence. For example: How frequently doyou watch the MTV television channel?

__ Every day

__ 5-6 times a week

__ 2-4 times a week

__ Once a week

__ Less than a week

__ Never

Attitude rating scales, such as the Likert Scale, Semantic Differential, and StapelScale, are also fixed-alternative questions.

The checklist question allows the respondent to provide multiple answers to a singlequestion. The respondent indicates past experience, preference, and the like merely bychecking off an item. In many cases the choices are adjectives that describe a particularobject. A typical checklist follows:

Please check which of the following sources of information about investments youregularly use, if any.

__ Personal advice of your brokers(s)

__ Brokerage newsletters

__ Brokerage research reports

__ Investment advisory service(s)

__ Conversations with other investors

__ Reports on the internet

__ None of these

__ Other (please specify)

Most questionnaires include a mixture of open-ended and closed questions. Each formhas unique benefits; in addition, a change of pace can eliminate respondent boredomand fatigue.

Phrasing Questions for Self-Administered, Telephone, and PersonalInterview Surveys

The means of data collection (personal interview, telephone, mail, or Internetquestionnaire) will influence the question format and question phrasing. In general,questions for mail and telephone surveys must be less complex than those utilized inpersonal interviews. Questionnaires for telephone and personal interviews should bewritten in a conversational style. Consider the following question from a personalinterview:

There has been a lot of discussion about the potential health threat to nonsmokers fromtobacco smoke in public building, restaurants, and business offices. How serious a

health threat to you personally is the inhaling of this secondhand smoke, often calledpassive smoking: Is it a very serious health threat, somewhat serious, not too serious,or not serious at all?

1. Very serious

2. Somewhat serious

3. Not too serious

4. Not serious at all

5. Don't know

THE ART OF ASKING QUESTIONS

In develop a questionnaire, there are no hard-and-fast rules. Fortunately, however,some guidelines that help to prevent the most common mistakes have "been developedfrom research experience.

1. Avoid Complexity: Use Simple, Conversational Language

Words used in questionnaires should be readily understandable to all respondent. Theresearcher usually has the difficult task of adopting the conversational language ofpeople from the lower educational levels without talking down to better-educatedrespondents. Remember, not all people have the vocabulary of a college student. Asubstantial number of Americans never go beyond high school.

Respondents can probably tell an interviewer whether they are married, single,divorced, separated, or windowed, but providing their "marital status" may present aproblem. Also, the technical jargon of corporate executives should be avoided whensurveying retailers, factory employees, or industrial users. "Marginal analysis,""decision support systems," and other words from the language of the corporate staffwill not have the same meaning to- or be understood by- a store owner / operator in aretail survey. The vocabulary in following question (from an attitude survey on socialproblems) is probably confusing for many respondents:

When effluents from a paper mill can be drunk, and exhaust from factory smokestackscan be breathed, then humankind will have done a good job in saving theenvironment... Don't you agree that what we want is zero toxicity and no effluents?

This lengthy question is also a leading question.

2. Avoid Leading and Loaded Questions

Leading and loaded questions are a major source of bias in question wording. LeadingQuestions suggest or imply certain answers. In a study of the dry-cleaning industry, thisquestion was asked:

Many people are using dry cleaning less because of improved wash-and-wear clothes.How do you feel wash-and-wear clothes have affected your use of dry-cleaningfacilities in the past 4 years?

_______Use less ______No change __________Use more

The potential "bandwagon effect" implied in this question threatens the study's validity.

Loaded questions suggest a socially desirable answer or are emotionally charged.Consider the following:

In light of today’s farm crisis, it would be in the public's best interest to have thefederal government require labeling of imported meat.

_____Strongly ____Agree ____Uncertain ____Disagree ____Strongly disagree

Answers might be different if the loaded portion of the statement, "farm crisis" hadanother wording suggesting a problem of less magnitude than a crisis. A televisionstation produced the following 10-second spot asking for viewer feedback:

We are happy when you like programs on Channel 7. We are sad when you dislikeprograms on Channel 7. Write to us and let us know what you think of ourprogramming.

Most people do not wish to make others sad. This question is likely to elicit only positivecomments. Some answers to certain questions are more socially desirable than others.For example, a truthful answer to the following classification question might be painful

Where did you rank academically in your high school graduating class?

___Top quarter ___2nd quarter ___3rd quarter ___4th quarter

When taking personality tests, respondents frequently are able to determine whichanswers are most socially acceptable, even though those answers do not portray theirtrue feelings.

3. Avoid Ambiguity: Be a Specific as Possible

Items on questionnaires are often ambiguous because they are too general. Considerindefinite words such as often, usually, regularly, frequently, many, good, fair, and poor.Each of these words has many meanings. For one person, frequent reading of Fortunemagazine may be reading six or seven issues a year; for another it may be two issues a

year. The word fair has a great variety of meanings; the same is true for many indefinitewords.

Questions such as the following should be interpreted with care:

How often do you feel that you can consider all of the alternatives before making adecision to follow a specific course of action?

___Always ___Fairly ___Occasionally ___Seldom ___Never often

In addition to utilizing words like occasionally, this question asks respondents togeneralize about their decision-making behaviour. The question is not specific. Whatdoes consider mean? The respondents may have a tendency to provide stereotyped"good" management responses rather than to describe their actual behavior. People'smemories are not perfect. We tend to remember the good and forget the bad.

4. Avoid Double- Barreled Items

A question covering several issues at once is referred to as double-barreled and shouldalways be avoided. It's easy to make the mistake of asking two questions rather thanone. For example:

Please indicate if you agree or disagree with the following statement: "I have called insick or left work to golf". Which reason is it - calling in sick or leaving work (perhapswith permission) to play golf?

When multiple questions are asked in one question, the results may be exceedinglydifficult to interpret. For example, consider the following question from a magazinesurvey entitled – "How Do You Feel about Being a Woman?":

Between you and your husband, who does the housework (cleaning, cooking,dishwashing, laundry) over and above that done by any hired help?

I do all of it

I do almost all if it

I do over half of it

We split the work fifty-fifty

My husband does over half of it

The answers to this question do not tell us if the wife cooks and the husband dries thedishes.

5. Avoid Making Assumptions

Consider the following question:

Should Mary's continue its excellent gift-wrapping program?

___Yes ___ No

The question contains the implicit assumption that people believe the gift-wrappingprogram is excellent. By answering yes, the respondent implies that the program is, infact, excellent and that things are just fine as they are. By answering no, he or sheimplies that the store should discontinue the gift wrapping. The researcher should notplace the respondent in that sort of bind by including an implicit assumption in thequestion.

6. Avoid Burdensome Questions That May Tax the Respondent's Memory

A simple fact of human life is that people forget. Researchers writing questions aboutpast behavior or events should recognize that certain questions may make seriousdemands on the respondent's memory. Writing questions about prior events requires aconscientious attempt to minimize the problem associated with forgetting.

It many situations, respondents cannot recall the answer to a question. For example, atelephone survey conducted during the 24-hour period following airing of the SuperBowl might establish whether the respondent watched the Super Bowl and then ask: "Doyou recall any commercials on that program?" If the answer is positive, the interviewermight ask: "what brands were advertised?" These two questions measure unaidedrecall, because they give the respondent no clue as to the brand of interest.

What is the Best Question Sequence?

The order of questions, or the question sequence, may serve several functions for theresearcher. If the opening questions are interesting, simple to comprehend, and easy toanswer, respondents' cooperation and involvement can be maintained throughout thequestionnaire. Asking easy-to-answer questions teaches respondents their role andbuilds confidence; they know this is a researcher and not another salesperson posing asan interviewer. If respondents' curiosity is not aroused at the outset, they can becomedisinterested and terminate the interviewer. A mail research expert reports that a mailsurvey terminates the interview. A mail research expert reports that a mail surveyamong department store buyers drew an extremely poor return. However, when someintroductory questions related to the advisability of congressional action on pendinglegislation of great importance to these buyers were placed first on the questionnaire, asubstantial improvement in response rate occurred. Respondents completed all the-questions, not only those in the opening section.

In their attempts to "warm up" respondents toward the questionnaire dependentresearchers frequently ask demographic or classification questions at the beginning ofthe questionnaire. This is generally not advisable. It may embarrass or threatenrespondents. It is generally better to ask embarrassing questions at the middle or end of

the questionnaire, after rapport has been established between respondent andinterviewer.

Sequencing specific questions before asking about broader issues is a common cause oforder bias. For example, bias may arise if questions about a specific clothing store areasked prior to those concerning the general criteria for selecting a clothing store.Suppose a respondent who indicates in the first portion of a questionnaire that theshops at a store where parking needs to be improved. Later in the questionnaire, toavoid appearing inconsistent, she may state that parking is less important a factor thanshe really believes it is. Specific questions may thus influence the more general ones.Therefore, it is advisable to ask general questions before specific questions to obtain thefreest of open ended responses. This procedure, known as the funnel technique, allowsfor researcher to understand the respondent’s frame of reference before asking morespecific questions about the level of the respondent’s information and the intensity ofhis or her opinions.

One advantage of internet surveys is the ability to reduce order bias by having thecomputer randomly order questions and/or response alternatives. With completerandomization, question order is random and respondents see response alternatives inrandom positions. Asking a question that doesn’t apply to the respondent or that therespondent is not qualified to answer may be irritating or may cause a biased responsebecause the respondent wishes to please the interviewer or to avoid embarrassment.Including a filter question minimizes the chance of asking questions that areinapplicable. Asking "where do you generally have cheque-cashing problems in Delhi"may elicit a response even though the respondent has not had any cheque-cashingproblems and may simply wish to please the interviewer with an answer. A filterquestion such as:

Do you ever have a problem cashing a cheque in Delhi? ___Yes ___No

would screen out the people who are not qualified to answer.

Another form of filter question, the pivot question, can be used to obtain incomeinformation and other data that respondents may be reluctant to provide. For example,a respondent is asked.

"Is your total family income over Rs.75,000?" IF NO, ASK...

"Is it over or under Rs.50,000?" IF UNDER, ASK…

"Is it over or under Rs.25,000?"

So, the options are

1. Over Rs.75,000

2. Rs.50,001 - Rs.75,000

3. Rs.25,001 - Rs.50,000

4. Under Rs.25,001

Structuring the order of questions so that they are logical will help to ensure therespondent’s cooperation and eliminate confusion or indecision. The researchermaintains legitimacy by making sure that the respondent can comprehend therelationship between a given question and the overall purpose of the study.

What is the best layout?

Good layout and physical attractiveness are crucial in mail, Internet, and other self-administered questionnaires. For different reasons it is also important to have a goodlayout in questionnaires designed for personal and telephone interviews.

LAYOUT OF TRADITIONAL QUESTIONNAIRES

The layout should be neat and attractive, and the instructions for the interviewer shouldbe clear. Often money can be spent on an incentive to improve the attractiveness andquality of the questionnaire.

Mail questionnaires should never be overcrowded. Margins should be of decent size,white space should be used to separate blocks of print, and any unavoidable columns ofmultiple boxed should be kept to a minimum. All boldface capital letters should easy tofollow.

Questionnaires should be designed to appear as brief and small as possible. Sometimesit is advisable to use a booklet form of questionnaire, rather than a large number ofpages stapled together.

In situations where it is necessary to conserve space on the questionnaire or to facilitateentering the data into a computer or tabulating the data, a multiple-grid layout may beused. In this type of layout, a question is followed by corresponding responsealternatives arranged in a grid or matrix format.

Experienced researchers have found that is pays to phrase the title of the questionnairecarefully. In self-administered and mail questionnaires a carefully constructed title mayby itself capture the respondent’s interest, underline the important of the research("Nationwide Study of Blood donors"), emphasize the interesting nature of the study("Study of Internet Usage"), appeal to the respondent’s ego ("Survey among TopExecutives"), or emphasize the confidential nature of the study ("A Confidential Surveyamong…"). The researcher should take steps to ensure that the wording of the title willnot bias the respondent in the same way that a leading question might.

When an interviewer is to administer the questionnaire, the analyst can design thequestionnaire to make the job of following interconnected questions much easier by

utilizing instruction, directional arrows, special question formats, and other tricks of thetrade.

SUMMARY

Many novelists write, rewrite, and revise certain chapters, paragraphs, and evensentences of their books. The research analyst lives in a similar world. Rarely does onewrite only a first draft of a questionnaire. Usually, the questionnaire is tried out on agroup that is selected on a convenience basis and that is similar in makeup to the onethat ultimately will be sampled. Researchers should select a group that is not toodivergent from the actual respondents. (e.g. business students as surrogates for businesspeople), but it is not necessary to get a statistical sample for protesting. The protestingprocess allows the researchers to determine if the respondents have any difficultyunderstanding the questionnaire and whether there are any ambiguous or biasedquestions. This process is exceedingly beneficial. Making a mistake with 25 or 50subjects can avert the disaster of administering an invalid questionnaire to severalhundred individuals.

KEY TERMS

· Open ended response questions· Fixed alternative questions· Leading question· Loaded question· Double-barreled question· Funnel technique· Filter question· Pretesting

QUESTIONS

1. What is the difference between leading question and loaded question?

2. Design an open end question to measure a reaction to a particular advertisement.

3. Design a complete a questionnaire to evaluate job satisfaction.

4. Develop a checklist to consider in questionnaire construction.

- End of Chapter -

LESSON – 14

MEASUREMENT

OBJECTIVES

· To know what is to be measured· To define the operation definition and scale measurement· To distinguish among nominal, ordinal, interval, and ratio scales· To understand the criteria of good measurement· To discuss the various methods of determining reliability· To discuss the various methods of assessing validity

STRUCTURE

· Measurement· Scale measurement· Types of scale· Criteria for good measurement

MEASUREMENT

Measurement is an integral part of the modern world. Today we have progressed in thephysical sciences to such as extent that we are now able to measure the rotation of adistant star, the attitude in micro-inches and so on. Today such a precise physicalmeasurement is very critical. In many business situations, the majority of themeasurements are applies to things that are much more abstract than attitude or time.The accurate measurement is essential for effective decision making. The purpose of thischapter is to provide with a basic understanding of the measurement process and rulesneeded for developing sound scale measurements.

In management research, measurement is viewed as the integrative process ofdetermining the amount (intensity) of information about constructs, concepts or objectsof interest and their relationship to a defined problem or opportunity. It is important tounderstand the two aspects of measurement one is construct development, whichprovides necessary and precise definition which begins the research process calledproblem definition in turn determine what specific data should be collected. Another isscale measurement means how the information is collected with reference to construct.In other words, the goal of construct development is to precisely identify and definewhat is to be measured including dimensions. In turn, the goal of scale measurement isto determine how to precisely measure the constructs.

Regardless of whether the researcher is attempting to collect primary data or secondarydata, all data can be logically classified as under.

a) State-of-Being Data

When the problem requires collecting responses that are pertinent to the physical,demographical or socioeconomic characteristics of individuals, objects or organizations,the resulting raw data are considered as state-of-being data. This data represent factualcharacteristics that can be verified through several sources other than the personsproviding the information.

b) State-of-Mind Data

This represents that mental attributes of individuals that are not directly observable oravailable through some other external sources. It exists only within the minds of people.The researcher has to ask a person to respond the stated questions. Examples arepersonality traits, attitudes, feelings, perceptions, beliefs, awareness level, preferences,images etc.

c) State-of-Behavior Data

This represents an individuals or organizations current observable actions or reactionsor recorded past actions. A person may categorically ask the past behavior. This can bechecked using external secondary sources, but that is very difficult process in terms oftime, effort and accuracy.

d) State-of-Intension Data

This represents individuals or organizations expressed plans of future behavior. Againthis also collected by asking carefully defined questions. Like the above data, this alsovery difficult to verify through external, secondary sources, but verification is possible.

With the background information about the type of data which are collected, thefollowing pages will be very useful in understanding the concepts of scale measurement.

SCALE MEASUREMENT

Scale measurement can be defined as the process of assigning a set of descriptions torepresent the range of possible responses to a question about a particular object orconstruct. Scale measurement directly determines the amount of raw data that can beascertained from a given questioning or observation method. This attempts to assigndesignated degrees of intensity to the responses, which are commonly referred to asscale points. The researcher can control the amount of raw data that can be obtainedfrom asking questions by incorporating scale properties or assumption in scale points.There are four scaling properties that a researcher can use in developing scales namelyassignment, order distance and origin.

1. Assignment (also referred to as description or category property): It is theresearchers’ employment of unique description to identity each object within a set, e.g.,the use of numbers, colors, yes & no responses.

2. Order refers to the relative magnitude between the raw responses. It establishes andcreates hierarchical rank-order relationship coming objects, e.g., 1st place is better than4th place.

3. Distance, is the measurement the express the exact difference between the tworesponses. This allows the researcher and respondent to identify, understand, andaccurately express absolute difference between objects, e.g., Family A has 3 children andFamily B has 6 children.

4. Origin, refers to the use of a unique starting as being "true zero" e.g., askingrespondent his or her weight or current age, market share of specific brand.

TYPES OF SCALES

While scaling properties determine the amount of raw data that can be obtained fromany scale design, all questions and the scale measurement can be logically andaccurately classified as one of four basic scale types: nominal, ordinal, integral or ratio.A scale may be defined as any series of items that are arranged progressively accordingto value or magnitude, into which an item can be placed according to its quantification.

The following table represents the relationship between types of scales & scalingproperties:

1. Nominal Scale

In business research, nominal data are probably more widely collected than any other. Itis the simplest type of scale and also the most basic of the four types of scale designs. Insuch a scale, the numbers serve as labels to identify persons, objects or events. Nominalscales are the least powerful of the four data types. They suggest no order or distancerelationship and have no arithmetic origin. This scale allows the researcher only tocategorize the raw responses into mutually exclusive and collectively exhaustive. In thenominal scale, the only operation is the counting of numbers in each group. An exampleof typical nominal scale in business research is the coding of males as 1 and females as 2.

Example 1:

Please indicate your current marital status.

____Married ____Single ___Never married ___Widowed

Example 2:

How do you classify yourself?

____Indian ___American ___Asian ___Black

2. Ordinal Scale

As the name implies, these are ranking scales. Ordinal data include the characteristics ofthe nominal data plus an indicator of order, means, this data activates both areassignment and order scaling properties. The researcher can rank-order the rawresponses into a hierarchical pattern. The use of ordinal data scale implies a statementof "greater than" or "less than" without stating how much greater or less. Examples ofordinal data include opinion and preference scales. A typical ordinal scale in businessresearch asks respondents to rate career opportunities, brands, companies etc., asexcellent, good, fair or poor.

Example 1:

Which of the following one category best describes your knowledge about computers?

1) Excellent 2) Good 3) Basic 4) Little 5) No knowledge

Example 2:

Among the listed below, please indicate top three preference using 1, 2, 3 as yourchoice in the respective source provided:

By post

By courier

By telephone

By speed post

By internet

By person

Also to be noted is that the individual ranking can be combined and get a collectiveranking of a group.

3. Interval Scales

The structure of this scale not only show the assignment, order scaling properties butalso the distance property with interval scale, researchers can identity not only sometype of hierarchical order among to raw data but also the specific differences betweenthe data. The classic example of this scale is the Fahrenheit temperature scale. If atemperature is 80 degree, it cannot be said that it is twice as hot as 40 degree. Thereason is that 0 degree does not represent the lack of temperature, but a relative pointon the Fahrenheit scale. Similarly, when this scale is used to measure psychologicalattributes, the researcher can comment on the magnitude of differences or compare theaverage differences but cannot determine the actual strength of attitude toward anobject. However many attitude scales are presumed to be interval scales. Interval scalesare more powerful than nominal and ordinal scales. Also they are quicker to completeand it is convenient for researcher.

Example 1:

Into which of the following categories does your income fall?

1. Below 5000

2. 5000 - 10,000

3. 10,000 - 15,000

4. 15,000 - 25,000

5. above 25,000

Example 2:

Approximately how long you lived in the current address?

1. Less than 1 year

2. 1-3 years

3. 4-6 years

4. More than 6 years

4. Ratio Scales

This is the only scale that simultaneously activates all four scaling properties. A ratioscale tends to be the most sophisticated scale in the sense that it allows not only toidentify the absolute differences between each represents but also absolutecomparisons.

Examples of ratio scales are the commonly used physical dimensions such as height,weight, distance, money value and population counts. It is necessary to remember thatratio scale structures are designed to allow a "zero" or "true state of nothing" response tobe a valid raw response to the question. Normally, the ratio scale requests thatrespondents give a specific singular numerical value as their response, regardless ofwhether or not a set of scale points used. The following are the examples of ratio scales:

Example 1:

Please circle the numbers of children below 18 years of ages in your house?

0 1 2 3 4 5

Example 2:

In past seven days, how many times did you go to retail shop?

____ number of times

Mathematical and Statistical Analysis of Scales

The type of scale that is utilized in business research will determine the form ofstatistical analysis. For example certain operations can be conducted only if a scale, of aparticular nature. The following will show the relationship between scale types andmeasures of central tendency and dispersion.

Here,

A - Appropriate

More A - More appropriate

Most A - Most appropriate

IA - Inappropriate

Criteria for good measurement

There are four major criteria for evaluating measurement: reliability, validity, sensitivityand practicality.

1. Reliability

It refers to the extent to which a scale can reproduce the same measurement results inrepeated trials. Reliability applies to a measure when similar results are obtainedovertime across situations. Broadly defined, reliability is the degree to which measuresare free from error and therefore yield consistent results. As discussed in the earlierchapter the error in scale measurements leads to lower scale reliability. Two dimensionsunderline the concept of reliability: one is repeatability and the other is internalconsistency.

First, the test-retest method involves administrating the same scale or measure to thesame respondents at two separate times to test for stability. If the measure is stable overtime, the test, administered under the same conditions each time, should obtain similarresults. The high stability correlation or consistency between the two measures at time 1and 2 indicates a high degree of reliability.

The second dimension of reliability concerns the homogeneity of the measure. TheSplit-half technique can be used when the measuring tool has many similarquestions or statements to which subjects can respond. The instrument is administeredand the results are separated by item into even and odd numbers or randomly selectedhalves. When the two halves are correlated, if the result of the correlation is high, theinstrument is said to be high reliability in internal consistency.

The Spearman-Brown Correction Formula is used to adjust the effect of testlength and to estimate reliability of the whole set. But, this approach may influence theintegral consistency because of the way in which the test is split. In order to overcomeKuder - Richardson Formula (KR 20) and Cronbach's Coefficient Alpha aretwo frequently used examples. The KR 20 is the method from which alpha wasgeneralized and is used to estimate reliability for dichotomous items. Cronbach's alphahas the most utility for multi-scale items at the interval level of measurement.

The third perspective on reliability considers how much error may be introduced bydifferent investigators or different samples of items being studied. In other words, theresearcher creates two similar yet different scale measurements for the given construct.An example of this is the scoring of Olympic skaters by a panel of judges.

2. Validity

The purpose of measurement is to measure what it intend to measure; but this is not assimple as it sounds at first. Validity is the ability of a measure to measure what it isproposed to measure. If it does not measure what it is designated to measure, there willbe problems. To assess the validity there are second ways which are discussed hereunder.

Face validity or Content validity, refers to the subjective agreement amongprofessionals that a scale logically appears to reflect accurately what it intend tomeasure. When it appears evident to experts that the measure provides adequatecoverage of the concept, a measure has face validity.

Criterion - Related validity reflects the success of measures used for prediction orestimation. Criterion validity may be classified as either concurrent validity orpredictive validity, depending on the time sequence in which the 'new' measurementscale and the criterion measure are correlated. If the new measure is taken at the sametime as the criterion measure and shown to be valid, then it has concurrent validity.Predictive validity is established when a new measure predicts a future event. These twomeasures differ only on the basis of time.

Construct validity is established by the degree to which a measure confirms thehypotheses generated from theory based on concepts. It implies the empirical evidencegenerated by a measure with the theoretical logic. To achieve this validity, theresearcher may use convergent validity (should converge with similar measure) ordiscriminant validity (when it has low correlation with the measures of dissimilarconcepts.)

3. Sensitivity

It is an important concept, particularly when changes in attitude or other — hypotheticalconstructs are under investigation. It refers to an instruments ability to accuratelymeasure variability in stimuli or responses. A dichotomous response category such as"agree" or "disagree" does not allow attitude change. But the scale staring from "stronglyagree", "agree", "neither agree nor disagree", "disagree" and "strongly disagree"increases the sensitivity.

4. Practicality

It can be defined in terms of economy, convenience and interpretability. This means thescientific requirements for the measurement process is called reliable and valid, while

operational requirements called it as practical where the above mentioned three aspectsare more important.

SUMMARY

This paper outlined the importance of the measurement. Different types of scales havebeen dealt in detail. This chapter has given the criteria for a good measurement.

KEY TERMS

· Nominal scale· Ordinal scale· Integral scale· Ratio scale· Reliability· Split-half Technique· Spearman-Brown Correction Formula· Kuder - Richardson Formula (KR 20)· Cronbach's Coefficient Alpha· Validity· Face validity· Content validity· Criterion - Related validity - concurrent validity or predictive validity· Construct validity· Sensitivity· Practicality

QUESTIONS

1. What are different types of data in the attitude measurement could be collected?

2. Discuss the measurement scaling properties.

3. Explain different scales of measurement.

4. Is the statistical analysis is based on the type of scale? Explain.

5. What do you mean by good measurement?

6. Explain various methods of reliability and validity.

- End of chapter -

LESSON – 15

ATTITUDE MEASUREMENT AND SCALING TECHNIQUES

OBJECTIVES

· To understand the definition of attitude· To learn the techniques for measuring attitudes

STRUCTURE

· Techniques for measuring attitude· Physiological measures of attitude· Summated rating method· Numerical scale· Graphic rating scale

ATTITUDE DEFINED

There are many definitions for the term attitude. An attitude is usually viewed as anenduring disposition to respond consistently in a given manner to various aspects of theworld, including persons, events, and objects. One conception of attitude is reflected inthis brief statement: "Sally loves working at Sam's. She believes it's clean, convenientlylocated, and has the best wages in town She intends to work there until she retires”. Inthis short description are three components of attitude: the affective, the cognitive,and the behavioral.

The affective component reflects an individual's general feelings or emotion towardan object. Statements such as "I love my job", "I liked that book, A Corporate Bestiary”,and "I hate apple juice" - reflect the emotional character of attitudes.

The way one feels about a product, a person, or an object is usually tied to one‘s beliefsor cognitions. The cognitive component represents one's awareness of andknowledge about an object. A woman might feel happy about her job because she"believes that the pay is great" or because she knows "that my job is the biggestchallenge in India."

The third component of an attitude is the behavioral component. Intention andbehavioral expectations are included in this component, which therefore reflects apredisposition to action.

Techniques for Measuring Attitudes

A remarkable variety of techniques have been devised to measure attitudes part, thisdiversity stems from the lack, of consensus about the exact definite of the concept.Further, the affective, cognitive, and behavioral component an attitude may bemeasured by different means. For example, sympathetic nervous system responses may

be recorded using physiological measures to measure affect but they are not goodmeasures of behavioral intentions. Direct verbal statements concerning affect, belief, orbehavior are utilized to measure behavioral intent. However, attitudes may also bemeasured indirectly by using the qualitative explanatory techniques. Obtaining verbalstatements from respondents generally requires that the respondent perform a task suchas ranking, rating, sorting, or making a choice or a comparison.

A ranking task requires that the respondents rank order a small number of items onthe basis of overall preference or some characteristic of the stimulus. Rating asks therespondents to estimate the magnitude of a characteristic or quality that an objectpossesses. Quantitative scores, along a continuum that has been supplied to therespondents, are used to estimate the strength of the attitude or belief. In other words,the respondents indicate the position, on a scale, where they would rate the object.

A sorting technique might present respondents with several product concepts,printed on cards, and require that the respondents arrange the cards into a number ofpiles or otherwise classify the product concepts. The choice technique, choosing oneof two or more alternatives, is another type of attitude measurement. If a respondentchooses one object over another, the researcher can assume that the respondent prefersthe chosen object over the other.

The most popular techniques for measuring attitudes are presented in this chapter.

Physiological Measures of Attitudes

Measures of galvanic skin response, blood pressure, and pupil dilation and otherphysiological measures may be utilized to assess the affective component of attitudes.They provide a means of measuring attitudes without verbally questioning therespondent. In general, they can provide a gross measure of like or dislike, but they arenot sensitive measures for identifying gradients of an attitude.

Attitude Rating Scales

Using rating scales to measure attitudes is perhaps the most common practice inbusiness research. This section discusses many rating, scales designed to enablerespondents to report the intensity of their attitudes.

Simple Attitude Scales

In this most basic form, attitude scaling requires that an individual agree or disagreewith a statement or respond to a single question. For example, respondents in a politicalpoll may be asked whether they agree or disagree with the statement "The presidentshould run for re-election", or an individual might be asked to indicate whether he likesor dislikes labor unions. Because this type or self-rating scale merely classifiesrespondents into one of two categories, it has only the properties of a nominal scale.This, of course, limits the type of mathematical analysis that may be utilized with thisbasic scale. Despite the disadvantages, simple attitude scaling may be used when

questionnaires are extremely long, when respondents have little education, or for otherspecific reasons.

Most attitude theorists believe that attitudes vary along continua. An early attituderesearcher pioneered the view that the task of attitude scaling is to measure the distancefrom "good" to "bad", "low" to "high", "like" to "dislike , and so on. Thus the purpose ofan attitude scale is to find an individual's position on the continuum. Simple scales donot allow for making fine distinctions in attitudes. Several scales have been developed tohelp make more precise measurements.

Category Scales

Some rating scales have only two response categories: agree and disagree. Expandingthe response categories provides the respondent more flexibility in the rating task. Evenmore information is provided if the categories are ordered according to a descriptive orevaluative dimension. Consider the questions below:

How often is your supervisor courteous and friendly to you?

___Never ___Rarely ___Often ___Very often

Each of these category scales is a more sensitive measure than a scaled with only tworesponse categories. Each provides more information.

Wording is an extremely important factor in the usefulness of these scales. Exhibit 14.1shows some common wordings for category scales.

Summated Ratings Method: The Likert Scale

Business researchers' adaptation of the summated ratings method, developed by RensisLikert, is extremely popular for measuring attitudes because the method is simple toadminister. With the Likert scale, respondents indicate their attitudes by checkinghow strongly they agree or disagree with carefully constructed statements that rangefrom very positive to very negative toward the attitudinal object. Individuals generallychoose from five alternatives: strongly agree, agree, uncertain, disagree, and stronglydisagree; but the number of alternatives may range from three to nine.

Consider the following example from a study on mergers and acquisitions:

Mergers and acquisitions provide a faster means of growth than internal expansions.

Strongly Disagree Disagree Uncertain Agree Strongly agree

(1) (2) (3) (4) (5)

To measure the attitude, researchers assign scores or weights to the alternativeresponses. In thus example, weights of 5, 4, 3, 2, and 1 are assigned to the answers. (Theweights, shown in parentheses, would not be printed questionnaire). Because thestatement used as an example is positive towards the attitude, strong agreementindicates the most favorable attitudes on the statement and is assigned a weight of 5. If anegative statement toward the object (such as "Your access to copy machines is limited")were given the weights would be reversed, and "strongly degree" would be assigned theweight of 5. A single scale item on a summated rating scale is an ordinal scale.

A Likert scale may include several scale items to form an index. Each statement isassumed to represent an aspect of a common attitudinal domain For example, Exhibit14.2 shows the items in a Likert scale to measure attitudes toward a management byobjectives program. The total score is the summation of the weights assigned to anindividual's response.

For example:

Here are some statements that describe how employees might feel about the MBO(management by objectives, form of management. Please indicate your agreement ordisagreement for each statement. Please encircle the appropriate number to indicatewhether you:

1 - Strongly Agree 2 – Agree 3 – Neutral 4 – Disagree 5 - Strongly Disagree

Circle one and only one answer for each statement. There are no right or wronganswers to these questions:

In Likert's original procedure, a large number of statements are generated and then anitem analysis is performed. The purpose of the item analysis is to ensure that finalitems evoke a wide response and discriminate among those with positive and negativeattitudes. Items that are poor because they lack clarity or elicit mixed response patternsare eliminated from the final statement list. However, many business researchers do notfollow the exact procedure prescribed by Likert. Hence, many business researches donot follow the exact procedure prescribed by Likert. Hence, a disadvantage of the Likert-type summated rating method is that it is difficult to know what a single summatedscore means. Many patterns of response to the various statements can produce the sametotal score. Thus, identical total scores may reflect different "attitudes" becauserespondents endorsed different combinations of statements.

Semantic Differential

The semantic differential is a series of attitude scales. This popular attitude-measurement technique consists of presenting an identification of a company, product,brand, job, or other concept, followed by a series of seven-point bipolar rating scales.Bipolar adjectives, such as "good" and "bad", "modern" and "old-fashioned", or "clean"and "dirty," anchor the beginning and end (or poles) of the scale.

Modern_____:______ :_____:______:_____:_____ :_____ Old-Fashioned

The subject makes repeated judgments of the concept under investigation on each of thescales.

The scoring of the semantic differential can be illustrated by using the scale bounded bythe anchors "modern" and "old-fashioned." Respondents are instructed to check theplace that indicates the nearest appropriate adjective. From left to right, the scaleintervals are interpreted as extremely modern, very modern, slightly modern, bothmodern and old-fashioned, slightly old-fashioned, very old-fashioned, and extremelyold-fashioned. A weight is assigned to each position on the rating scale. Traditionally,scores are 7, 6, 5, 4, 3, 2, 1, or +3, +2, +1, 0, -1, -2, -3.

Many researchers find it desirable to assume that the semantic differential providesinterval data. This assumption, although widely accepted, has its critics, who argue thatthe data have only ordinal properties because the weights are arbitrary. Depending onwhether the data are assumed to be interval or ordinal, the arithmetic mean or themedian is utilized to plot the profile of one concept, product, unit, etc., compared withanother concept, product, or units.

The semantic differential technique was originally developed by Charles Osgood andothers as a method for measuring the meaning of objects or the "semantic space" ofinterpersonal experience." Business researchers have found the semantic differentialversatile and have modified it for business applications.

Numerical Scales

Numerical scales have numbers, rather than "semantic space" or verbal descriptions asresponse options to identify categories (response positions). If the scale items have fiveresponse positions, the scale is called a 5-point numerical scale; with seven responsepositions, it is called a 7-point numerical scale, and so on.

Consider the following numerical scale:

Now that you've had your automobile for about one year, please tell us how satisfiedyou are with your Ford Ikon:,

Extremely Satisfied Extremely Dissatisfied

7 6 5 4 3 2 1

This numerical scale utilizes bipolar adjectives in the same manner as the semanticdifferential.

Constant-Sum Scale

If a Parcel Service company wishes to determine the importance of the attributes ofaccurate invoicing, delivery as promised, and price to organizations that use its servicein business-to-business marketing. Respondents might be asked to divide a constantsum to indicate the relative importance of the attributes. For example:

Divide 100 points among the following characteristics of a delivery service accordingto how important each characteristic is to you when selecting a delivery company.

Accurate invoicing___

Delivery as promised___

Lower price___

The constant-sum-scale works best with respondents with high educational levels. Ifrespondents follow instructions correctly, the results approximate interval measures. Asin the paired-comparison method, as the number of stimuli increases this techniquebecomes more complex.

Stapel Scale

The Stapel scale was originally developed in the 1950s to measure the direction andintensity of an attitude simultaneously. Modern versions of the scale use a singleadjective as a substitute for the semantic differential when it is difficult to create pairs ofbipolar adjectives. The modified Stapel scale places a single adjective in the center of aneven number of numerical values (for example, ranging from +3 to -3). It measures howclose to or how distant from the adjective a given stimulus is perceived to be.

The advantages and disadvantages of the Stapel scale are very similar to those of thesemantic differential. However, the Stapel scale is markedly easier to administer,especially over the telephone. Because the Stapel scale does not requires bipolaradjectives, as does the semantic differential, the Stapel scale is easier to construct.Research comparing the semantic differential with the Stapel scale indicates that resultsfrom the two techniques are largely the same.

Graphic Rating Scale

A graphic rating scale presents respondents with graphic continuum. The respondentsare allowed to choose any point on the continuum to indicate their attitudes. Typically, arespondent's score is determined by measuring the length (in millimeters) from one endof the graphic continuum to the point marked by the respondent. Many researchersbelieve scoring in this manner strengthens the assumption that graphic rating scales ofthis type are interval scales. Alternatively, the researcher may divide the line intopredetermined scoring categories (lengths) and record respondent's marks accordingly.In other words, the graphic rating scale has the advantage of allowing the researchers tochoose any interval they wish for purposes of scoring. The disadvantage of the graphicrating scale is that there are no standard answers.

Thurstone Equal-Appearing Interval Scale

In 1927, Louis Thurstone, an early pioneer in attitude research, developed the conceptthat attitudes vary along continua and should be measured accordingly. Construction ofa Thurstone scale is a rather complex process that requires two stages. The first stage isa ranking operation, performed by judges, who assigns scale values to attitudinalstatements. The second stage consists of asking subjects to respond to the attitudinalstatements.

The Thurstone method is time-consuming and costly. From a historical perspective it isvaluable, but its current popularity is low, because it is rarely utilized in most appliedbusiness research.

Scales Measuring Behavioral Intentions and Expectations

The behavioral component of an attitude involves the behavioral expectations of anindividual toward an attitudinal object. Typically, this represents an intention or atendency to seek additional information. Category scales that measure the behavioralcomponent of an attitude attempt to determine a respondent's "likelihood" of action orintention to perform some future action, as in the following examples:

How likely is it that you will change jobs in the next six months

· I definitely will change.· I probably will change.· I might change.· I probably will not change.· I definitely will not change.

I would write a letter to my congressmen or other government official in support ofthis company if it were in a dispute with government.

· Extremely likely· Very likely

· Somewhat likely· Likely, about 50-50 chance· Somewhat unlikely· Very unlikely· Extremely unlikely

Behavioral Differential

A general instrument, the behavioral differential, has been developed to measure thebehavioral intentions of subjects toward an object or category of objects. As in thesemantic differential, a description of the object to be judged is placed on the top of asheet, and the subjects indicate their behavioral intentions toward this object on a seriesof scales. For example, one item might be:

A 25-year-old female commodity broker

Would: ______:_____ :_____ :_____ :_____ :_____:Would not

ask this person for advice.

Ranking

People often rank order their preferences. An ordinal scale may be developed by askingrespondents to rank order (from most preferred to lease preferred) a set of objects orattributes. It is not difficult for respondents to understand the task of rank ordering theimportance of fringe benefits or arranging a set of job tasks according to preference.

Paired Comparisons

The following question is the typical format for asking about paired comparisons.

I would like to know your overall opinion of two brands of adhesive bandages. Theyare Curad brand and Band-Aid brand. Overall, which of these two brands - Curad orBand-Aid - do you think is the better one? Or are both the same?

Curad is better____

Band-Aid is better____

They are the same____

Ranking objects with respects to one attribute is not difficult if only a few concepts oritems are compared. As the number of items increases, the number of comparisonsincreases geometrically. If the number of comparisons is too great, respondents maybecome fatigued and no longer carefully discriminate among them.

Sorting

Sorting tasks requires that respondents indicate their attitudes or beliefs by arrangingitems.

SUMMARY

This chapter describes the technique for measuring attitude. This paper outlined theimportance of the attitude.

KEY TERMS

· Attitude· Affective component· Cognitive component· Behavioral component· Ranking· Rating· Category scale· Likert scale· Semantic differential scale· Numerical scale· Constant sum scale· Stapel scale· Graphic rating scale· Paired comparison

QUESTIONS

1. What is an attitude?

2. Distinguish between rating and ranking. Which is a better attitude measurement?Why?

3. Describe the different methods of scale construction, pointing out the merits anddemerits of each.

4. What advantages do numerical scales have over semantic differential scales?

- End of chapter -

LESSON – 16

STATISTICAL TECHNIQUES

OBJECTIVES

· Know the nature of Statistical study· Recognize the importance of Statistics as also its limitations· Differentiate descriptive Statistics from inferential Statistics.

STRUCTURE

· Major characteristics of statistics· Description statistics· Inferential statistics· Central tendency of data· Use of different average· Types of frequency distribution· Measure of dispersion

INTRODUCTION

Business researchers edit and code data to provide input that results in tabulatedinformation that will answer research question. With this input, the results can beproduced statistically and logically. Aspects of Statistics are important if the quantitativedata are to serve their purpose. If Statistics, as a subject, is inadequate and consists ofpoor methodology, we would not know the right procedure to extract from the data theinformation they contain. On the other hand, if our figures are defective in the sensethat they are inadequate or inaccurate, we would not reach the right conclusions eventhough our subject is well developed. With this brief introduction, let us first see howStatistics has been defined.

Major characteristics of statistics:

1. Statistics are aggregates of facts. This means that a single figure is not Statistics. Forexample, national income of a country for a single year is not Statistics but the same fortwo or more years is.

2. Statistics are affected by a number of factors. For example, sale of a product dependson a number of factors such as its price, quality, competition, the income of theconsumers, and so on.

3. Statistics must be reasonably accurate. Wrong figures, if analyzed, will lead toerroneous conclusions. Hence, it is necessary that conclusions must be based onaccurate figures.

4. Statistics must be collected in a systematic manner. If data are collected in ahaphazard manner, they will not be reliable and will lead to misleading conclusions.

5. Finally, Statistics should be placed in relation to each other. If one collects dataunrelated to each other, then such data will be confusing and will not lead to any logicalconclusions. Data should be comparable over tin e and over space.

Subdivisions in Statistics

The statisticians commonly classify this subject into two broad categories: descriptivestatistics and inferential statistics.

1. Descriptive Statistics

As the name suggests descriptive statistics includes any treatment designed to describeor summaries the given data, bringing out their important features. These statistics donot go beyond this. This means that no attempt is made to infer anything that pertainsto more than the data themselves. Thus, if someone compiles the necessary data andreports that during the financial year 2000-2001, there were 1500 public limitedcompanies in India of which 1215 earned profits and the remaining 285 companiessustained losses, his study belongs to the domain of descriptive Statistics. He mayfurther calculate the average profit earned per company as also average loss sustainedper company. This set of calculations too is a part of descriptive statistics.

Methods used in descriptive statistics may be called as descriptive methods. Underdescriptive methods, we learn frequency distribution, measures of central tendency, thatis, averages, measures of dispersion and skewness.

2. Inferential Statistics

Although descriptive Statistics is an important branch of Statistics and it continues to beso, its recent growth indicates a shift in emphasis towards the methods of Statisticalinference. A few examples may be given here. The methods of Statistical inference arerequired to predict the demand for a product such as tea or coffee for a company for aspecified year or years. Inferential Statistics are also necessary while comparing theeffectiveness of a given medicine in the treatment of any disease.

Again, while determining the nature and extent of relationship between two or morevariables like the number of hours studied by students and their performance in theirexaminations, one has to take recourse to inferential Statistics.

Each of these examples is subject to uncertainty on account of partial, incomplete, orindirect information. In such cases, the Statistician has to judge the merits of all possiblealternatives in order to make the most realistic prediction or to suggest the mosteffective medicine or to establish a dependable relationship and the reasons for thesame. In this text, we shall first discuss various aspects of descriptive Statistics. This willbe followed by the discussion on different topics in inferential Statistics. The latter willunderstandably be far more comprehensive than the former.

CENTRAL TENDENCY OF DATA

In many frequency distributions, the tabulated values show small frequencies at thebeginning and at the end and very high frequency at the middle of the distribution. Thisindicates that the typical values of the variable lie near the central part of thedistribution and other values cluster around these central values. This behavior of thedata about the concentration of the values in the central part of the distribution is calledcentral tendency of the data. We shall measure this central tendency with the help ofmathematical quantities. A central value which 'enables' to comprehend in a singleeffort the significance of the whole is known as Statistical Average or simply Average. Infact, an average of a statistical series is the value of the variable which is representativeof the entire distribution and, therefore, gives a measure of central tendency.

Measures of Central Tendency

There are three common measures of central tendency

I. Mean

II. Median

III. Mode

The most common and useful measure of central tendency is, however the Mean. In thefollowing articles the method of calculation of various measures of central tendency willbe discussed. In all such discussion we need a very useful notation known asSummation.

Choice of a Suitable Average

The different statistical average has different characteristics. There is no all-purposeaverage. The choice of a particular average is usually determined by the purpose ofinvestigation. Within the framework of descriptive statistics, the main requirement is toknow what each average means and then select the one that fulfils the purpose at hand.The nature of distribution also determines the type of average to be used.

Generally the following points should be kept in mind while making a choice of averagefor use

1. Object

The average should be chosen according to the object of enquiry. If all the values in aseries are to be given equal importance, then arithmetic mean will be a suitable choice.To determine the most stylish or most frequently occurring item mode should be foundout. If the object is to determine an average that would indicate its position or ranking inrelation to all the values, naturally, median should be the choice. If small items are to begiven greater importance than the big items, geometric mean is the best mean.

2. Representative

The average chosen should be such that it represents the basic characteristics of thedistribution.

3. Nature of form of data

If the frequently distribution is symmetrical or nearly symmetrical X, M or Mo may beused almost interchangeably. If there are open-end class intervals, mean cannot becalculated definitely. In a closed frequently distribution of unequal class intervals, it isimpossible to determine mode accurately. If there are a few values, it may not bepossible to determine mode. Mean will not give a representative picture, if there are fewextremely large or small values at either end of the array, and yet the great majority ofthe values concentrate around a narrow band. In a variable of non-continuous type,median or mode may give a value that actually exists in the data.

Davis' Test: Arithmetic mean is considered as an appropriate average for use for datawhich has a symmetrical distribution or even if it has a moderate degree of asymmetry.Prof. George Davis has devised a test which is:

If this coefficient works out to be more than +0.20, the distribution is symmetricalenough to use arithmetic mean.

4. Characteristics of Average

While choosing a suitable average for a purpose, the merits and demerits of variousaverages should always be considered and that average which fits into the purpose mostshould be preferred over others. The following points should be given due considerationin the process of selection of an average.

(i) In certain commonly encountered applications, the mean is subject to less samplingvariability than the median or mode.

(ii) Given only the original observations, the median is sometimes easiest to calculate.Sometimes when there is no strong advantage for the mean, this advantage is enough toindicate the use of the median.

(iii) Once a frequency distribution has been formed, the mode and the median are modequickly calculated than the mean. Moreover, when some classes are open-ended themean cannot be calculated from the frequency distribution.

(iv) The median is not a good measure when there are very few possible values for theobservations as with number of children or size of family.

(v) The mode and the median are relatively little affected by 'extreme' observations.

(vi) Calculations of geometric mean and harmonic mean is difficult as it involves theknowledge of logarithms and reciprocals.

Hence "the justification of employing them (averages) must be determined by an appealto all the facts and in the light of the peculiar characteristics of the different types".

Uses of Different Averages

Different averages, due to their inherent characteristics are appropriate in differentcircumstances. Thus, their use may be guided by the purpose at hand or circumstancesin which one is. Here a brief discussion is being made of uses of different statisticalaverages:

1. Arithmetic Average

The arithmetic average used in the study of a social, economic or commercial problemlike production, income, price, imports, exports, etc. The central tendency if thesephenomena can best be studied by taking out an arithmetic average. Whenever we talkof an 'average income' or 'average production' or 'average price' we always meanarithmetic average of all these things. Whenever there is no indication about the type ofthe average to be used, arithmetic average is computed.

2. Weighted Arithmetic Average

When it is desirable to give relative importance to the different items of a series,weighted arithmetic average is computed. If it is desired to compute per capitaconsumption of a family, due weights should be assigned to children, males and females.This average is also useful in constructing numbers. The weighted average should beused in the following cases:

a) If it is desired to have an average of whole group, which is divided into anumber of sub-classes, widely divergent from each other?

b) When items falling in various sub-classes change in such a way that theproportion which the items bear among themselves also undergoes a change.

c) When combined average has to be computed.

d) When it is desired to calculate to find an average of ratios, percentages or rates.

3. Median

Median is especially applicable to cases which are not capable of precise quantitativestudies such as intelligence, honesty, etc. It is less applicable in economic or businessstatistics, because there is lack of stability in such data.

4. Mode

The utility of mode is being appreciated more and more day by day. In r the sciences ofBiology and Meteorology it has been found to be of great value. In commerce andindustry it is gaining very great importance. Whenever as shop-keeper wants to stockthe goods he sells, he always looks to the modal size of those goods. Model size of shoes,is of great importance to the businessman dealing in ready-made garments or shoes.Many problems of production are related with mode. Many business establishmentsthese days are engaging their attention in keeping statistics of their sale ascertain theparticulars of the modal articles sold.

5. Geometric Mean

Geometric mean can advantageously be used in the construction of index numbers. Itmakes the index numbers reversible and gives equal weight to equal ratio of changes.This average is also useful in measuring the growth of population, because increases ingeometric progression. When there is wide dispersion in a serious, geometric mean is auseful average.

6. Harmonic Mean

This average is useful in the cases where time, rate and prices are involved. When it isdesired to give the largest weight to the smallest item, this average is used.

Summation Notation (∑)

The symbol ∑ (read: sigma) means summation.

If x1, x2, x3, …, xn be the n values of a variable x. Then their sum x1 +x2+ x3+ …+ xn isshortly written as

Similarly, the sum w1x1+w2x2+ …+ wnxn is denoted by

Some important results

There are three types of mean

1. Arithmetic Mean (AM)

2. Geometric Mean (GM)

3. Harmonic Mean (HM)

Of the three means, Arithmetic Mean is most commonly used. In fact, if no specificmention be made, by Mean we shall always refer to Arithmetic Mean (AM) and calculateaccordingly.

Simple Arithmetic Mean

Definition: The Arithmetic Mean (x ̅) of a given series of values, say x1, x2, x3, …, xn, isdefined as the sum of these values divided by their total number; thus

Weighted Arithmetic Mean is defined by:

Example 1: Find the AM of 3, 6, 24, and 48.

Solution: AM = (3 + 6 + 24 + 48) / 4 = 81/4 = 20.25

Weighted Arithmetic Mean

Definition: x1, x2, x3, …, xn be n values of a variable x, and if f1, f2, …, fn be their respectiveweights (or frequencies), then the weighted arithmetic mean is defined by

where, N = ∑f = total frequency

SKEWNESS

A frequency distribution is said to be symmetrical when the values of the variableequidistant from their mean have equal frequencies. If a frequency distribution is notsymmetrical, it is said to be asymmetrical or skewed. Any deviation from symmetry iscalled Skewness.

In the words of Riggleman and Frisbee: "Skewness is the lack of symmetry. When afrequency distribution is plotted on a chart, skewness present in the items tends to bedispersed more on one side of the mean than on the other".

Skewness may be positive or negative. A distribution is said to be positively skewed ifthe frequency curve has a longer tail towards the higher values of x, ie, if the 'frequencycurve gradually slopes down towards the high values of x.

For a positively skewed distribution, Mean (M) > Median (Me) > Mode (Mo)

A distribution is said to be negatively skewed if the frequency curve has a longer tailtowards the lower values of x.

For a negatively skewed distribution, Mean (M) < Median (Me) < Mode(Mo)

For a symmetrical distribution, Mean (M) = Median (Me) = Mode (Mo)

Measures of Skewness

The degree of skewness is measured by its coefficient. The common measures ofskewness are:

1. Pearson's first measure

Skewness = (Mean – Mode) / Standard Deviation

2. Pearson's second measure

Skewness = 3 x (Mean - Mode)/ Standard Deviation

3. Bowley's Measure

where Q1, Q2, Q3 are the first, second and third quartiles respectively.

4. Moment Measure

Skewness = m3 / σ3 = m3 / m23/2

where m2 and m3 are the second and third central moments and σ is the S.D.

All the four measure of Skewness defined above are independent of the units ofmeasurement.

Example:

Calculate the Pearson's measure of Skewness on the basis of Mean, Mode, and StandardDeviation.

Solution:

According to Pearson's first measure, Skewness = (Mean – Mode) / Standard Deviation

Here mid-values of the class-intervals are given. Assuming a continuous series, weconstruct the following table:

Types of Frequency Distributions

In general, frequency distributions that form a balanced pattern are called symmetricaldistributions, and those that form an unbalanced pattern are called skewed orasymmetrical distributions. In a symmetrical distribution frequencies go on increasingup to a point and then begin to decrease in the same fashion. A special kind ofsymmetrical distribution is the normal distribution; the pattern formed is not onlysymmetrical but also has the shape of a bell.

In a symmetrical distribution, mean median and mode coincide and they lie at thecentre of distribution. As the distribution departs from symmetry these three values arepulled apart. A distribution, in which more than half of the area under the curve is to theright side of the mode, is a positively skewed distribution. In a positively skeweddistribution, its right tail is longer than its left tail. Under such a distribution mean is

greater than the median, and the median is greater than the mode (M > Me > Mo), andthe difference between upper quartile and median is greater than the difference betweenmedian and lower quartile (Q3-Me > Me-Q1). In a negatively skewed distribution, morethan half of the area under the distribution curve is to the left side of the mode. In such adistribution the elongated tail us to the left and mean is less than the median andmedian is less than the mode (M < Me < Mo), and the difference between upper quartileand median is less than the difference between median and lower quartile (Q3-M < M-Q1).The following figures show these facts. The following table will also show these factsof Position of Average on Various Distributions.

Test of Skewness

In order to find out whether a distribution is symmetrical or skewed, the following factsshould be noticed:

1. Relationship between Averages

If in a distribution mean, median and mode are not identical, then it is a skeweddistribution. The greater is the difference between mean and mode more will be theskewness in the distribution.

2. Total of Deviations

If the sum of positive deviations from median or mode is equal to the sum of negativedeviation, then is no skewness in the distribution. The extent of difference between thesums of positive and negative deviations from median or mode will determine the extentof skewness in the data.

3. The distance of partition values from median

In a symmetrical distribution Q1 and Q2, D1 and D9 and P10 and P90 are equidistant frommedian. In an asymmetrical distribution it is not so.

4. The frequencies on either side of the mode

In an asymmetrical distribution, frequencies on either side of the mode are not equal.

5. The curve

When the data are plotted on a graph paper, the curve will not be bell-shaped, or whencut along a vertical line through the centre, the two halves will not be identical.Conversely stated, in the absence of skewness in the distribution:

(i) Values of mean, median and mode will coincide.

(ii) Sum of the positive deviations from the median or mode will be equal to the sum ofnegative deviations.

(iii) The two quartiles, deciles one and nine, and percentile ten and ninety will beequidistant from the median.

(iv) Frequencies on the either side of the mode will be equal.

(v) Data when plotted on a graph paper will take a bell-shaped form.

Measures of Skewness

To find out the direction and the extent of symmetry in a series statistical measures ofskewness are calculated, these measures can be absolute or relative. Absolute measuresof skewness tell us the extent of asymmetry and whether it is positive or negative. Theabsolute skewness can be known by taking the deference between mean and mode.Symbolically,

Absolute SK = X - Mo

If the value of mean is greater than the mode (M > Mo) skewness will be positive. Incase the value of mean is less than the mode (M < Mo) skewness will be negative. Thegreater is the amount of skewness, the more the mean and mode differ because of theinfluence of extreme items. The reason why the difference between mean and mode istaken for the measure of skewness is that in a symmetrical distribution, both the valuesalong with median coincide, but in an asymmetrical distribution, there will be adifference between the mean and mode.

Thus the difference between the mean and the mode, whether positive or negative,indicates that the distribution is asymmetrical. However such absolute measure ofskewness is unsatisfactory, because:

(1) It cannot be used for comparison of skewness in tow distributions if they are indifferent units, because the difference between the mean and the mode will be in termsof the units of distribution.

(2) The difference between the mean and mode may be more in one series and less inanother, yet the frequency curves of the two distributions may be similarly skewed. Forcomparison, the absolute measures of skewness are changed to relative measures, whichare called Coefficient of Skewness.

There are four measures of relative skewness. They are:

1. The Karl Pearson's Coefficient of Skewness

2. The Bowley's Coefficient of Skewness.

3. The Kelly's Coefficient of Skewness

4. Measure of skewness based onmoments. Measures of Skewness

1. The Karl Pearson's Coefficient of Skewness

Karl Pearson has given a formula, for relative measure of Skewness. It is known as KarlPearson's Coefficient of Skewness or Pearsonian Coefficient of Skewness. The formula isbased on the difference between the mean and mode divided by the standard deviation.The coefficient is represented by J

If in a particular frequency distribution, the mode is ill-defined, the coefficient ofSkewness can be determined by the following changed formula.

This is based on the relationship between different averages in a moderatelyasymmetrical distribution. In such a distribution:

The Pearsonian coefficient of skewness has the interesting characteristic that it will bepositive when the mean is larger than the mode or median, and it will be negative whenthe arithmetic mean is smaller than the mode or median. In a symmetrical distribution,the value of Pearsonian coefficient of skewness will be zero.

There is no theoretical limit to this measure, however, in practical the value given by thisformula is rarely very high and usually lies between ±∞. The direction of the skewness isgiven by the algebraic sign of the measure; if it is plus then the skewness is positive, if itis minus, the skewness is negative. The degree of skewness is obtained by the numericalfigure such as 0.9, 0.4, etc.

Thus this formula gives both the direction as well as the degree of skewness. There isanother relative measure of skewness also based on the position of averages. In this, thedifference between two averages is divided by the mean deviation. The formula is:

These formulas are not very much used in practice, because of demerits of meandeviation.

DISPERSION

Measures of Dispersion

An average nay give a good idea of the type of data, but it alone can't reveal all thecharacteristics of data. It cannot tell us in what manner all the values of the variable arescattered / dispersed about the average.

Meaning of Dispersion

The Variation or Scattering or Deviation of the different values of a variable from theiraverage is known as Dispersion. Dispersion indicates the extent to which the values varyamong themselves. Prof. W.I. King defines the term, 'Dispersion' as it is used to indicate

the facts that within a given group, the items differ from another in size or in otherwords, there is lack of uniformity in their sizes. The extent of variability in a given set ofdata is measured by comparing the individual values of the variable with the average allthe values and then calculating the average of all the individual differences.

Objectives of Measuring Variations

1. To serve as a basis for control of the variability itself.

2. To gauge the reliability of an average

3. To serve as a basis for control of the variability itself

Types of Measures of Dispersion

There are two types of measures of dispersion. The first, which may be referred to asDistance Measures, describes the spread of data in terms of distance between the valuesof selected observations. The second are those which are in terms of an averagedeviation from some measure of central tendency.

Absolute and Relative Measures of Dispersion

Measures of absolute dispersion are in the same units as the data whose scatter theymeasure. For example, the dispersion of salaries about an average is measured in rupeesand the variation of time requires for workers to do a job is measured in minutes orhours. Measures of absolute dispersion cannot be used to compare the scatter in onedistribution with that in another distribution when the averages of the distributionsdiffer in size or the units of measure differ in kind. Measures of relative dispersion showsome measure of scatter as a percentage or coefficient of the absolute measure ofdispersion. They are generally used to compare the scatter in one distribution with thescatter in other. Relative measure of dispersion is called coefficient of dispersion.

Methods of Measuring Dispersion

There are two meanings of dispersion, as explained above. On the basis of these twomeanings, there are two mathematical methods of finding dispersion, i.e. methods oflimits and methods of moment. Dispersion can also be studied graphically. Thus, thefollowing are the methods of measuring dispersion:

I. Numerical Methods

1. Methods of Limits

i. The Range

ii. The Inter-Quartile Range

iii. The Percentile Range

2. Methods of Moments

i. The first moment of dispersion or mean deviation

ii. Second moment of dispersion from which standard deviation iscomputed

iii. Third moment of dispersion

3. Quartile Deviation

II. Graphic Method

Lorenz Curve

Range

The simplest measure of dispersion is the range of the data. The range is determined bythe two extreme values of the observations and it is simply the differences between thelargest and the smallest value in a distribution. Symbolically,

Range (R) = Largest value (L) - Smallest value (S)

Coefficient of Range (CR) = (Largest Value + Smallest Value) / (LargestValue - Smallest Value)

Quartile Deviation or Semi-Interquartile Range

Definition: Quartile Deviation (Q) is an absolute measure of dispersion and is defined byformula:

Q = (Q3 – Q1) / 2

Where, Q1 and Q2 are the first (or lower) and the third (or upper) quartiles respectively.Here Q3 – Q1 is the interquartile range and hence quartile deviation is called Semi-interquartile Range.

As it is based only on the Q1 and Q3, it does not take into account the variability of all thevalues and hence it is not very much used for practical purposes.

Example:

Find the quartile deviation of the following frequency distribution.

Daily wages: 10-15 15-20 20-25 25-30 30-35

No of workers: 6 12 18 10 4

Solution:

N/4 = 50/4 = 12.5 and 3N/4 = 37.5.

By simple interpolation,

(Q1 – 15) / (20 – 15) = (12.5 – 6) / (18 – 6)

(Q1 – 15) / 5 = 6.5 / 12

Q1 = (6.5 / 12) x 5 + 15

Q1 = 17.71

Similarly,

(Q3 – 25) / (30 – 25) = (37.5 – 36) / (46 – 36)

(Q3 – 25) / 5 = 1.5 / 10

Q3 = 0.15 x 5 + 25

Q3 = 25.75

Hence, Quartile Deviation,

(Q3 – Q1) / 2 = (25.75 – 17.71) / 2 = 4.02

MEAN DEVIATION

(or Average Deviation or Mean Absolute Deviation)

Definition: Mean Deviation of a series of values of a variable is the arithmetic mean ofall the absolute deviations (i.e., difference without regard to sign) from any one of itsaverages (Mean, Median or Mode, but usually Mean or Median). It is an absolutemeasure of dispersion.

Mean deviation of a set of n values x1, x2,…, xn about their AM is defined by

where x = values or mid-value accordingly to data being ungrouped or grouped, and xbar = Mean

where M = Median and d= x – M = Value (or mid value) – Median.

Similarly, we can define Mean Deviation about Mode.

Note: The expression |d| is read as mod. d and gives only numerical or absolute value ofd without regard to sign. Thus,

|-3| = 3, |-4| = 4, |0.56| = 0.56

The reason for taking only the absolute and not the algebraic values of the deviation isthat the algebraic sum of the deviations of the value from their mean is zero.

Example:

Find the Mean Deviation about the Arithmetic Mean of the numbers 31, 35, 29, 63, 55,72, 37.

Solution:

Arithmetic Mean = (31 + 35 + 29 + 63 + 55 + 72 + 37) / 7 = 322/7 = 46

Calculation of absolute Deviations

The required Mean Deviation about the Mean = ∑|d| / n = 104 / 7 = 14.86

Advantages

Mean deviation is based on all the values of the variable and sometimes gives fairly goodresult as a measure of dispersion. However the practice of neglecting signs and taking

absolute deviations for the calculation of the mean Deviation seems rather unjustifiedand this makes algebraic treatment difficult.

STANDARD DEVIATION

It is the most important absolute measures of Dispersion. Standard Deviation of setvalues of a variable is defined as the positive square root of arithmetic mean of thesquares of all deviations of the values from their arithmetic mean. In short it is thesquare root of the mean of the squares of deviations from mean.

If x1, x2, ...,xn be a series of values of a variable and x bar their AM, then S.D (σ) isdefined by

The square of Standard Deviation is known as Variance i.e., Variance σ2 = (SD)2

SD is often defined as the positive square root of Variance.

Example:

Find the standard deviation of the following numbers: 1, 2, 3, 4, 5, 6, 7, 8, and 9

Solution:

The deviations of the numbers from the AM 5 are respectively -4, -3, -2, -1, 0, 1, 2, 3, and4

The squares of the deviations from AM are 16, 9, 4, 1, 0, 1, 4, 9, and 16

Therefore,

= (16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16) / 9 = 2.58

Advantages and Disadvantages

Standard Deviation is the most important and widely used among the measures ofdispersion and it possesses almost all the requisites of a good measure of dispersion. Itis rigidly defined and based on all the values of the variable.

It is suitable for algebraic treatment. SD is less affected by sampling fluctuations thanany other absolute measure of dispersion.

SD is difficult to understand. The process of squaring the deviations from their AM andthen taking the square-root of the AM of these squared deviations is a complicatedaffair.

The calculation of SD can be made easier by changing the origin and the scaleconveniently.

Relative Measures of Dispersion

Absolute measures expressed as a percentage of a measure of a control tendency givesrelative measures of dispersion. Relative measures are independent of the units ofmeasurement and hence they are used for the comparison of dispersion of two or moredistributions given in different units.

Co-efficient of Variation

Co-efficient of variation is the first important relative measure of dispersion and isdefined by the following formula:

Co-efficient of variation = Standard Deviation / Mean x 100

Co-efficient of variation is thus the ratio of the Standard deviation to the mean,expressed as a percentage. In the words of Karl Pearson, Co-efficient of Variation is thepercentage variation in the mean.

Coefficient of Quartile Deviation

Co-efficient of quartile deviation is a relative measure of dispersion and is defined by

Coefficient of Quartile Deviation = Quartile Deviation / Median x 100

Coefficient of Mean Deviation

It is a relative measure of dispersion. Co efficient of Mean Deviation is defined by

Coefficient of Mean Deviation = Mean Deviation / (Mean or Median) x 100

Example:

Find the Mean Deviation about the Median in respect of the following numbers: 46, 79,26, 85, 39, 65, 99, 29, 56, and 72. Find also the Co efficient of Mean Deviation.

Solution:

By arranging the given numbers in ascending order of magnitude, we obtain 26, 29, 39,46, 56, 65, 72, 79, 85, and 99.

Median = [(n+1)/2]th value = [11/2]th value = 5.5th value = (5th value + 6th value) / 2 =(56+65)/2 = 60.5

Absolute deviation of the values from the Median 60.5 is respectively…

34.5, 31.5, 21.5, 14.5, 4.5, 4.5, 11.5, 18.5, 24.5, and 38.5

Therefore, Mean Deviation (MD) about the Median

=(34.5+31.5+21.5+14.5+4.5+4.5+11.5+18.5+24.5+38.5)/2 = 20.4

Co-efficient of MD = MD / Median x 100 = 20.4 / 60.5 x 100 = 33.72%

KURTOSIS

Kurtosis in Greek means ‘bulginess’. The degree of kurtosis of a distribution is measuredrelative to the peakedness of a normal curve. The measure of kurtosis indicates whetherthe curve of the frequency distribution is flat or peaked.

Kurtosis is the peakedness of a frequency curve. In two or more distributions havingsame average, dispersion and skewdness, one may have higher concentration of valuesnear the mode, and its frequency curve will show sharper peak than the others. Thischaracteristic of frequency distribution is known as Kurtosis.

Kurtosis is measured by the coefficient β2, which is defined by the formula

β2 = m4 / m22 = m4 / σ4 or by γ2 = β2 – 3, where m4 and m2 are the 2nd and 4th controlmoments, and σ = SD.

A distribution is said to be Platy-kurtic, Meso-kurtic, and Lepto-kurtic corresponding toβ2 < 3, β2 = 3, or β2 > 3.

Accordingly,

It’s Platy-kurtic, if m4 / σ4 < 3

It’s Meso-kurtic, if m4 / σ4 = 3

It’s Lepto-kurtic, if m4 / σ4 > 3

Karl person in 1905 introduced the terms MESOKURTIC, LEPTOKURTIC, andPLATYKURTIC. A peaked curve is called "Leptokurtic" and a flat topped curve is termed"Platykurtic". These are evaluated by comparison with intermediate peaked curve. Thesethree curves differ widely in regard to convexity.

Example:

Calculate the measures of the following distribution:

Solution:

V1 = ∑fd / N = 0/100 = 0

V2 = ∑fd2 / N = 446/100 = 4.46

V3 = ∑fd3 / N = -36/100 = -0.36

V4 = ∑fd4 / N = 4574/100 = 45.74

μ4 = V4 – 4V1V3 + 6V12V2 – 3V14

= 45.74 – 4(0)(-0.36) + 6(0)2(4.46) – 3(0)4

α4 or α2 = V4/ V22 = 45.74 / 4.462 = 2.3

The value of β2 is less than 3, hence the curve is Platykurtic.

SUMMARY

This chapter helps us to know the nature of the statistical study. This chapter recognizesthe importance of statistics and also its limitations. The differences between descriptivestatistics and inferential statistics are dealt in detail.

KEY WORDS

· Descriptive Statistics

· Inferential Statistics· Mean· Standard Deviation· Median· Mean Deviation· Mode· Arithmetic Mean· Geometric Mean· Averages· Dispersion· Skewness· Mean deviation· Kurtosis

REVIEW QUESTIONS

1. Explain the special features of measures of central tendency.

2. How will you choose an 'average'?

3. What is dispersion? State its objectives. Explain the various types measures ofdispersion.

4. Explain the various methods of measuring dispersion.

5. Differentiate standard deviation from mean deviation.

6. Define 'skewdness'. How will you measure it?

7. Explain the application of averages in research.

- End of Chapter -

LESSON – 17

MEASURES OF RELATIONSHIP

OBJECTIVES

To study simple, partial and multiple correlation and their application in research

STRUCTURE

· Measure of relationship· Correlation· Properties of correlation co-efficient· Methods of studying correlations· Application of correlation

MEASURES OF RELATIONSHIP

The following statistical tools measure the relationship between the variables analyzedin social science research:

(i) Correlation

· Simple correlation· Partial correlation· Multiple correlation

(ii) Regression

· Simple regression· Multiple regressions

(iii) Association of attributes

CORRELATION

Correlation measures the relationship (positive or negative, perfect) between the twovariables. Regression analysis considers relationship between variables and estimatesthe value of another variable, having the value of one variable. Association of Attributesattempts to ascertain the extent of association between two variables.

Aggarwal Y.P., in his book 'Statistical Methods' has defined coefficient of correlation as,"a single number that tells us to what extent two variables or things are related and towhat extent variations in one variable go with variations in the other".

Richard Levin in his book, 'Statistics for Management' has defined correlation analysisas "the statistical tool that we can use to describe the degree to which one variable islinearly related to another". He has further stated that, "frequently correlation analysisis used in conjunction with regression analysis to measure how well the regression lineexplains the variation of the dependent variable 'r'. Correlation can also be used by itself,however, to measure the degree of association between two variables".

Srivastava U.K. Shenoy G.V, and Sharma S.C, in their book 'Quantitative Techniques forManagerial Decision' have stated that, "correlation analysis is the statistical techniquethat is used to describe the degree to which one variable is related to another.

Frequently correlation analysis is also used along with the regression analysis tomeasure how well the regression line explains the variations of the dependent variable.The correlation coefficient is the statistical tool that is used to measure the mutualrelationship between the two variables".

Coefficient of correlation is denoted by 'r'.

The sign of 'r' shows the direction of the relationship between the two variables X and Y.Positive correlation reveals that there is a positive correlation between the two variables.Negative correlation reveals negative relationship. Levin states that if an inverserelationship exists — that is, if Y decreases as X increases — then ‘r’ will fall between 0and -1. Likewise, if there is a direct relationship (if Y increases as X increases), then ‘r’will be a value within the range of 0 to 1.

Aggarwal Y.P. has highlighted in his book 'Statistical Methods', the properties ofcorrelation and factors influencing the size of the correlation coefficient. The details aregiven below:

PROPERTIES OF THE CORRELATION COEFFICIENT

The range of correlation coefficient is from -1 through 0 to +1. The values of r = -1 and r= +1 reveal a case of perfect relationship, though the direction of relationship is negativein the first case, and positive in the second case.

The correlation coefficient can be interpreted in terms of r2. It is known as 'coefficient ofdetermination'. It may be considered as the variance interpretation of r2.

Example:

r = 0.5

r2 = 0.5 x 0.5 = 0.25. In terms of percentage, 0.25x100% = 25%

It refers that 25 percent of the variance in Y scores has been accounted for by thevariance in X.

The correlation coefficient does not change if every score in either or both distribution isincreased or multiplied by a constant.

Causality cannot be inferred solely as the basis of a correlation between two variables. Itcan be inferred only after conducting controlled experiments.

The direction of the relation is indicated by the sign (+ or -) of the correlation.

The degree of relationship is indicated by the numerical value of the correlation. A valuenear 1 indicates a nearly perfect relation, and a value near 0 indicates no relationship.

In a positive relationship both variables tend to change in the same direction: as Xincreases, Y also tends to increase.

The Pearson correlation measures linear (straight line) relationship.

A correlation between X and Y should not be interpreted as a cause-effect relationship.Two variables can be related without one having a direct effect on the other.

FACTORS INFLUENCING THE SIZE OF CORRELATION COEFFICIENT

1. The size of r is very much dependent upon the variability of measured values m thecorrelated sample. The greater the variability, the higher will be the correlation,everything else being equal.

2. The size of r is altered when researchers select extreme groups of subjects in order tocompare these groups with respect to certain behaviors. Selecting extreme groups onone variable increases the size of r over what would be obtained with more randomsampling.

3. Combining two groups which differ in their mean values on one of the variables is notlikely to faithfully represent the- true situation as far as the correlation is concerned.

4. Addition of an extreme case (and conversely dropping of an extreme case) can lead tochanges in the amount of correlation. Dropping of such a case leads to reduction in thecorrelation while the converse is also true.

TYPES OF CORRELATION

a) Positive or Negative

b) Simple, Partial and Multiple

c) Linear and Non-linear

a) Positive and Negative Correlations

Both the variables (X and Y) will vary in the same direction. If variable X increases,variable Y also will increase; If variable X decreases, variable Y also will decrease. Innegative correlation, the given variables will vary in opposite direction. If one variableincreases, other variable will decrease.

b) Simple, Partial and Multiple Correlations

In simple correlation, relationship between two variables are studied. In partial andmultiple correlations, three or more variables are studied. In multiple correlation, threeor more variables are simultaneously studied. In partial correlation, more than two

variables are studied, but the effect on one variable is kept constant and relationshipbetween other two variables is studied

c) Linear and Non-Linear Correlations

It depends upon the constancy of the ratio of change between the variables. In linearcorrelation the percentage change in one variable will be equal to the percentage changein another variable. It is not so in non-linear correlation.

METHODS OF STUDYING CORRELATION

a) Scatter Diagram Method

b) Graphic Method

c) Karl Pearson's Coefficient of Correlation

d) Concurrent Deviation Method

e) Method of Least Squares

Karl Pearson's Coefficient of Correlation

Procedure

i. Compute mean of the X series data

ii. Compute mean of the Y series data

iii. Compute deviations of X series from the mean of X. It is denoted as x.

iv. Square the deviations. It is denoted as x2.

v. Compute deviations of Y series from the mean of Y. It is denoted as y.

vi. Square the deviations. It is denoted as y2.

vii. Multiply deviation (X series, Y series) and compute total. It denoted as ∑xy.

The above values can be applied in the formula and correlation can be computed.

Karl Pearson's Coefficient of Correlation (r)

where,

dx = sum of deviations of X series from the assumed mean

dy = sum of deviations of Y series from the assumed mean

∑dxdy = total of deviations (X and Y series)

∑dx2 = deviations of X series from assumed mean are squared

∑dy2 = deviations of Y series from assumed mean are squared

N = Number of items

The above values can be applied in the above formula and correlation can be computed.

Correlation for the grouped data can be computed with the help of the followingformula:

In the above formula, deviations are multiplied by the frequencies. Other steps are thesame.

CALCULATION OF CORRELATION

► Raw Score Method

r = 0.7

► Deviation Score Method (using Actual Mean)

Calculate Karl Pearson’s Coefficient of Correlation from the following data:

Solution

Karl Pearson’s Correlation Coefficients:

Year Index ofProduction (X)

x = (X-Xmean) x2 No. of unemployed

(Y)y = (Y-

Ymean) y2 xy

1985 100 -4 16 15 0 0 0

1986 102 -2 4 12 -3 9 +61987 104 0 0 13 -2 4 01988 107 +3 9 11 -4 16 -121989 105 +1 1 12 -3 9 -31990 112 +8 64 12 -3 9 -241991 103 -1 1 19 +4 16 -41992 99 -5 25 26 +11 121 -55

∑X ∑x ∑x2 ∑Y ∑y ∑y2 ∑xy= 832 = 0 = 120 = 120 = 0 = 184 = -92

= ∑X / N = 832/8 = 104

= ∑Y / N = 120/8 = 15

r = -92 / (120 x 184)1/2 = -0.619

The Correlation between index of production and unemployed is negative.

► Calculation of Correlation Coefficient (using Assumed Mean)

Calculate Coefficient of Correlation from the following data:

Solution

RANK CORRELATION

It is a method of ascertaining co variability or the lack of it between the two variables.Rank correlation method is developed by the British Psychologist Charles EdwardSpearmen in 1904. Gupta S.P has stated that "the rank correlation method is used whenquantitative measures for certain factors cannot be fixed, but individual in the group canbe arranged in order thereby obtaining for each individual a number of indicatinghis/her rank in the group".

The formula for Rank Correlation

Rank – Difference Coefficient of Correlation (Case of no ties in ranks)

Rank Correlation,

= 1 – (6 x 38) / 5x(52-1) = 1 – 228/(5x24) = 1 – 1.9 = -0.9

Relationship between X and Y is very high and inverse. Relationship between Scores onTest I and Test II is very high and inverse.

Procedure for Assigning Ranks

First rank is given to the student secured highest score. For example, in Test I, student Fis given first rank, as his score is the highest. The second rank is given to the nexthighest score. For example, in Test I, student E is given second rank. Student A and Ghave similar scores of 20 each and they stand for 6th and 7th ranks. Instead of givingeither 6th or 7th ranks to both the students, the average of the two ranks [average of 6and 7] 6.5 is given to each of them. The same procedure is followed to assign ranks tothe scores secured by students in Test II.

Calculation of Rank Correlation when ranks are tied

Rank – Difference Coefficient of Correlation (in case of ties in ranks)

= 1 – [(6x24) / 10(102-1)] = 1 – [144/990] = 0.855

APPLICATION OF CORRELATION

Karl Pearson Coefficient of Correlation can be used to assess the extent of relationshipbetween motivation of export incentive schemes and utilization of such schemes byexporters.

Motivation and Utilization of Export Incentive Schemes – CorrelationAnalysis

Opinion scores of various categories of exporters towards motivation and utilization ofexport incentive schemes can be recorded and correlated by using Karl PearsonCoefficient of Correlation and appropriate interpretation may be given based on thevalue of correlation.

Testing of Correlation

't' test is used to test correlation coefficient. Height and weight of a random sample of sixadults is given.

It is reasonable to assume that these variables are normally distributed, so the KarlPearson Correlation coefficient is the appropriate measure of the degree of associationbetween height and weight.

r = 0.875

Hypothesis test for Pearson's population correlation coefficient

H0: p = 0 - this implies no correlation between the variables in the population

H1: p > 0 - this implies that there is positive correlation in the population (increasingheight is associated with increasing weight)

5% significance level

= 0.875 x [(6–2)1/2] / (1–0.8752) = 0.875 x 2 / 0.234 = 3.61

Table value of 5% significance level

4 degrees of freedom (n-2) = (6-2) = 2.132

Calculated value is more than the table value. Null hypothesis is rejected. There issignificant positive correlation between height and weight.

Partial Correlation

Partial Correlation is used in a situation where three and four variables involved. Therevariables such as age, height and weight are given. Here, partial correlation is applied.Correlation between height and weight can be computed by keeping age constant. Agemay be the important factor influences the strength of relationship between height andweight. Partial correlation is used to keep constant the effect age. The effect of one

variable is partially out from the correlation between other two variables. This statisticaltechnique is known as partial correlation.

Correlation between variables x and y is denoted as rxy

Partial correlation is denoted by the symbol r123. This is correlation between variables 1and 2, keeping 3rd variable constant.

where,

r123 = partial correlation between variables 1 and 2

r12 = correlation between variables 1 and 2

r13 = correlation between variables 1 and 3

r23 = correlation between variables 2 and 3

Multiple Correlation

Three or more variables are involved in multiple correlation. The dependent variable isdenoted by X1 and other variables are denoted by X2, X3 etc. Gupta S. P. has expressedthat "the coefficient of multiple linear correlation is represented by R1 and it is commonto add subscripts designating the variables involved. Thus R1.234 would represent thecoefficient of multiple linear correlation between X1 on the one hand, X2, X3 and X4 onthe other. The subscript of the dependent variable is always to the left of the point".

The coefficient of multiple correlation for r12, r13 and r23 can be expressed as follows:

Coefficient of multiple correlations for R1.23 is the same as R1.32. A coefficient of multiplecorrelation lies between 0 and 1. If the coefficient of multiple correlations is 1, it showsthat the correlation is perfect. If it is 0, it shows that there is no linear relationshipbetween the variables. The coefficients of multiple correlation are always positive in signand range from +1 to 0.

Coefficient of multiple determinations can be obtained by squaring R1.23.

Multiple correlation analysis measures the relationship between the given variables. Inthis analysis the degree of association between one variable considered as the dependentvariable and a group of other variables considered as the independent variables.

SUMMARY

This chapter outlined the significance in measuring the relationship. This chapterdiscuss the factors that affecting correlation. The different applications of correlationhave been dealt in detail.

KEY WORDS

· Measures of Relationship· Correlation· Simple correlation· Partial correlation· Multiple correlation· Regression· Simple regression· Multiple regressions· Association of Attributes· Scatter Diagram Method· Graphic Method

· Karl Pearson's Coefficient of Correlation· Concurrent Deviation Method· Method of Least Squares Karl Pearson's Coefficient of Correlation

REVIEW QUESTIONS

1. What are the different measures and their significance in measuring Relationship?

2. Discuss the factors affecting Correlation.

3. What are the applications of Correlation?

4. Discuss in detail on different types of Correlation.

REFERENCE BOOKS

1. Robert Ferber, Marketing research, New York: McGraw Hill Inc., 1976.

2. Chaturvedhi, J.C., Mathematical Statistics, Agra: Nok Jhonk Karyalaya, 1953.

3. Emony, C. William, Business Research Methods, Illinois, Irwin, Homewood. 1976.

- End of Chapter -

LESSON – 18

TABULATION OF DATA

STRUCTURE

· Table· Relations frequency table· Cross tabulation and stub-and-banner tables· Guideline for cross tabulation

INTRODUCTION

To get meaningful information from the data it is arranged in the tabular form.Frequency tables, histograms are simple form of tables.

Frequency Tables

Frequency table or frequency distribution is a better way to arrange data. It helps incompressing data. Though some information is lost, compressed data show a patternclearly. For constructing a frequency table, the data are divided into groups of similarvalues (class) and then record the number of observations that fall in each group.

Table 1: Frequency table on age-wise classification of respondents

The data of collection days are presented in the following table as a frequency table. Thenumber of classed can be increased by reducing the size of the class. The choice of classintervals is mostly guided by practical consideration rather than by rules. Class intervalsare made in such a way that measurements are uniformly distributed over the class andthe interval is not very large. Otherwise, the mid value will either overestimate orunderestimate the measurement.

Relative frequency tables

Frequency is total number of data points that fall within that class. Frequency of eachvalue can also be expressed as a fraction or percentage of the total number ofobservations. Frequencies expressed in percentage terms are known as relativefrequencies. A relative frequency distribution is presented in the table below.

Table 2: Relative frequency table on occupation-wise classification ofrespondents

It may be observed that the sum of all relative frequencies is 1.00 or 100% becausefrequency of each class has been expressed as a percentage of the total data.

Cumulative frequency tables

Frequency or one-way tables represent the simplest method for analyzing categoricaldata. They are often used as one of the exploratory procedures to review how differentcategories of values are distributed in the sample.

For example, in a survey of spectator interest in different sports, we could summarizethe respondents' interest in watching football in a frequency table as follows:

Table 3: Cumulative frequency table on Statistics about football watchers

The table above shows the number, proportion, and cumulative proportion ofrespondents who characterized their interest in watching football as either (1) Alwaysinterested, (2) Usually interested, (3) Sometimes interested, or (4) Never interested.

Applications

In practically every research project, a first "look" at the data usually includes frequencytables. For example, in survey research, frequency tables can show the number of malesand females who participated in the survey, the number of respondents from particularethnic and racial backgrounds, and so on. Responses on some labeled attitudemeasurement scales (e.g., interest in watching football) can also be nicely summarizedvia the frequency table. In medical research, one may tabulate the number of patientsdisplaying specific symptoms; in industrial research one may tabulate the frequency ofdifferent causes leading to catastrophic failure of products during stress tests (e.g.,which parts are actually responsible for the complete malfunction of television setsunder extreme temperatures?). Customarily, if a data set includes any categorical data,then one of the first steps in the data analysis is to compute a frequency table for thosecategorical variables.

Cross Tabulation and Stub-and-Banner Tables

Managers and researchers frequently are interested in gaining a better understanding ofthe differences that exist between two or more subgroups. Whenever they try to identifycharacteristics common to one subgroup but not common to other subgroups, (i.e. they

are trying to explain differences between the subgroups). Cross tables are used toexplain the difference between the subgroups.

Cross tabulation is a combination of two (or more) frequency tables arranged such thateach cell in the resulting table represents a unique combination of specific values ofcross tabulated variables. Thus, cross tabulation allows us to examine frequencies ofobservations that belong to specific categories on more than one variable.

By examining these frequencies, we can identify relations between cross tabulatedvariables. Only categorical variables or variables with a relatively small number ofdifferent meaningful values should be cross tabulated. Note that in the cases where wedo want to include a continuous variable in a cross tabulation (e.g., income), we can firstrecode it into a particular number of distinct ranges (e.g. low, medium, high).

Guidelines for Cross Tabulation

The most commonly used method of data analysis is cross tabulation. The followingguidelines will helpful to design proper cross tabulation,

1. The data should be in categorical form

Cross tabulation is applicable to data 1 which both the dependent and the independentvariables appear in categorical form. There are two types of categorical data.

One type (assume type A) consists of variables that can be measured only in classes orcategories. Like marital status, gender, occupation variables can be measured incategories not quantifiable (i.e. no measurable number).

Another type (say type B) variables, which can be measured in numbers, such as age,income. For this type the different categories are associated with quantifiable numbersthat show a progression from smaller values to larger values.

Cross tabulation is used on both types of categorical variables. However whenconstruction across tabulation is done using type B categorical variables, researchersfind it helpful to use several special steps to make such cross tabulations more effectiveanalysis tools.

1. If certain variable is believed to be influenced by some other variable, the former canbe considered to be a dependent variable and the later is called as independentvariable.

2. Cross tabulate an important dependent variable with one or more'explaining' independent variables.

Researchers typically cross tabulate a dependent variable of importance to the objectivesof the research project (such as heavy user versus light user or positive attitude versusnegative attitude) with one or more independent variables that the researchers believe

can help explain the variation observed in the dependent variable. Any two variables canbe used in a cross tabulation so long as they both are in categorical form, and they bothappear to be logically related to one another as dependent and independent variablesconsistent with the purpose and objectives of the research project.

3. Show percentage in a cross tabulation

In a cross tabulation researchers typically show the percentage as well as the actualcount s of the number of responses falling into the different cells of the table. Thepercentages more effectively reveal the relative sizes of the actual counts associated withthe different cells and make it easier for researchers to visualize the patterns ofdifferences that exist in the data.

Constructing and Interpreting a Cross Tabulation

After drawing the cross table the interpretations has to be drawn from the table. Itshould convey the meaning and findings from the table. In management researchinterpretations has more value. From the interpretations and findings managers takedecisions.

2x2 Tables

The simplest form of cross tabulation is the 2 by 2 table where two variables are"crossed," and each variable has only two distinct values. For example, suppose weconduct a simple study in which males and females are asked to choose one of twodifferent brands of soda pop (brand A and brand B); the data file can be arranged likethis:

The resulting cross tabulation could look as follows.

Each cell represents a unique combination of values of the two cross tabulated variables(row variable Gender and column variable Soda), and the numbers in each cell tell ushow many observations fall into each combination of values. In general, this table showsus that more females than males chose the soda pop brand A, and that more males thanfemales chose soda B. Thus, gender and preference for a particular brand of soda may berelated (later we will see how this relationship can be measured).

Marginal Frequencies

The values in the margins of the table are simply one-way (frequency) tables for allvalues in the table. They are important in that they help us to evaluate the arrangementof frequencies in individual columns or rows. For example, the frequencies of 40% and60% of males and females (respectively) who chose soda A (see the first column of theabove table), would not indicate any relationship between Gender and Soda if themarginal frequencies for Gender were also 40% and 60%; in that case they would simplyreflect the different proportions of males and females in the study. Thus, the differencesbetween the distributions of frequencies in individual rows (or columns) and in therespective margins inform us about the relationship between the cross tabulatedvariables.

Column, Row, and total Percentages. The example in the previous paragraphdemonstrates that in order to evaluate relationships between cross tabulated variableswe need to compare the proportions of marginal and individual column or rowfrequencies. Such comparisons are easiest to perform when the frequencies arepresented as percentages.

Evaluating the Cross Table

Researchers find it useful to answer the following three questions when evaluating crosstabulation that appears to explain differences in a dependent variable.

1. Does the cross tabulation show a valid or a spurious relationship?

2. How many independent variables should be used in the cross tabulation?

3. Are the differences seen in the cross tabulation statistically significant, or could theyhave occurred by chance due to sampling variation?

Each of this is discussed below.

Does the cross tabulation show a valid explanation?

If it is logical to believe that changes in the independent variables can cause changes inthe dependent variables, then the explanation revealed by the cross tabulation isthought to be a valid one.

Does the cross tabulation show a valid or a spurious relationship?

An explanation is thought to be a spurious one if the implied relationship between thedependent and independent variables does not seem to be logical.

Example: family size, income seem appear to be logically related to the householdconsumption of certain basic food products. However it may not be logical to relate thenumber of automobiles owned with the brand of toothpaste preferred, or to relate thetype of family pet with the occupation of the head of the family. If the independentvariable does not logically have an effect or influence on the dependent variable, therelationship that a cross tabulation seems to show may not be a valid cause and effectrelationship, and therefore may be a spurious relationship.

How many independent variables should be used?

When cross tabulating an independent variable that seems logically related to thedependent variable, what should researchers do if the results do not reveal a clear-cutrelationship?

Two possible courses of actions are available.

1. Try another cross tabulation, but this time using one of the other independentvariable hypothesized to be important when the study was designed.

2. A preferred course of action is to introduce each additional independent variablesimultaneously with rather than as an alternative to the first independent variable triedin the cross tabulation. By doing so it is possible to study the interrelationship betweenthe dependent variable and two or more independent variables.

SUMMARY

The data can be summarized in the form of table. Cross table given the meaning fullinformation from the raw data. The way of constructing cross tables and interpretingand evaluating is very important.

KEY WORDS

· Class· Frequency

· Relations frequency· Cumulative frequency· Marginal frequency· Cross table

REVIEW QUESTIONS

1. Why do we use cross tables?

2. How do you evaluate the cross table?

3. Define the guidelines for constructing the cross table

- End of Chapter -

LESSON – 19

STATISTICAL SOFTWARE

OBJECTIVES

· To learn the application of various statistical packages used for the managementresearch process

· To understand the procedures for performing the tests using SPSS

STRUCTURE

· Statistical packages· Statistical analysis using SPSS· t-test, F-test, chi-square test, Anova· Factor analysis

Statistical Packages

The following statistical software packages are widely used:

· STATA· SPSS· SAS

STATA

Stata, created in 1985 by Statacorp, is a statistical program used by many businesses andacademic institutions around the world. Most of its users work in research, especially inthe fields of economics, sociology, political science, and epidemiology.

Stata's full range of capabilities includes:

· Data management· Statistical analysis· Graphics· Simulations· Custom programming

SPSS

The computer program SPSS (originally, Statistical Package for the Social Sciences) wasreleased in its first version in 1968, and is among the most widely used programs forstatistical analysis in social science. It is used by market researchers, health researchers,survey companies, government, education researchers' and others. In addition tostatistical analysis, data management (case selection, file reshaping, creating deriveddata) and data documentation are features of the base software.

The many features of SPSS are accessible via pull-down menus (see image) or can beprogrammed with a proprietary 4GL "command syntax language". Command syntaxprogramming has the benefits of reproducibility and handling complex datamanipulations and analyses

Solve business and research problems using SPSS for Windows, a statistical and datamanagement package for analysts and researchers.

SPSS for Windows provides you with a broad range of capabilities for the entireanalytical process. With SPSS, you can generate decision-making information quicklyusing powerful statistics, understand and effectively present the results with high-quality tabular and graphical output, and share the results with others using a variety ofreporting methods, including secure Web publishing. Results from the data analysisenable you to make smarter decisions more quickly by uncovering key facts, patterns,and trends. An optional server version delivers enterprise-strength scalability,additional tools, security, and enhanced performance.

SPSS can be used for Windows in a variety of areas, including:

· Survey and market research and direct marketing· Academia· Administrative research· Medical, scientific, clinical, and social science research· Planning and forecasting· Quality improvement· Reporting and ad hoc decision making

· Enterprise-level analytic application development

In particular, apply SPSS statistics software to gain greater insight into the actions,attributes, and attitudes of peopleth - e customers, employees, students, or citizens.

Add more functionality as you need it

SPSS for Windows is a modular, tightly integrated, full-featured product line for theanalytical process — planning, data collecting, data access, data management andpreparation, data analysis, reporting, and deployment. Using a combination of add-onmodules and stand-alone software that work seamlessly with SPSS Base enhances thecapabilities of this statistics software. The intuitive interface makes it, easy to use - yet itgives you all of the data management, statistics, and reporting methods you need to do awide range of analysis.

Gain unlimited programming capabilities

Dramatically increase the power and capabilities of SPSS for Windows by using theSPSS Programmability Extension. This feature enables analytic and applicationdevelopers to extend the SPSS command syntax language to create procedures andapplications - and perform even the most complex jobs within SPSS. The SPSSProgrammability Extension is included with SPSS Base, making this statistics softwarean even more powerful solution.

Maximize market opportunities

The more competitive and challenging the business environment, the more you needmarket research. Market research is the systematic and objective gathering, analysis,and interpretation of information. It helps the organization identify problems andopportunities and allows for better-informed, lower-risk decisions.

For decades, solutions from SPSS Inc. have added value for those involved in marketresearch. SPSS solutions support the efficient gathering of market research informationthrough many different methods, and make it easier to analyze and interpret thisinformation and provide it to decision makers.

We offer solutions both to companies that specialize in providing market researchservices and to organizations that conduct their own market research. SPSS marketresearch solutions help you:

· Understand the market perception of the brand· Conduct effective category management· Confidently develop product features· Perform competitive analysis

With this insight, you or the clients can confidently make decisions about developingand marketing the products and enhancing the brand.

The heart of SPSS market research solution is dimensions product family. ThroughDimensions, the organization can centralize the creation and fielding of surveys in anymode and in any language, as well as the analysis and reporting phases of the research.

Dimensions data can be directly accessed using SPSS for Windows, which enables theanalysts to use SPSS' advanced statistical and graphing capabilities to explore the surveydata. Add-on modules and integrated stand-alone products extend SPSS' analytical andreporting capabilities. For example, analyze responses to open-ended survey questionswith SPSS Text Analysis for Surveys.

Maximize the value the organization receives from its Dimensions data by using anenterprise feedback management (EFM) solution from SPSS. EFM provides you with acontinuous means of incorporating regular customer insight into the businessoperations. Engage with current or prospective customers through targeted feedbackprograms or by asking questions during naturally occurring events. Then use theresulting insights to drive business improvement across the organization. SPSS' EFMsolution also enables you to integrate the survey data with transactional and operationaldata, so you gain a more accurate, complete understanding of customer preferences,motivations, and intentions.

Thanks to the integration among SPSS offerings, you can incorporate insights gainedthrough survey research in the predictive models created by the data mining tools. Youcan then deploy predictive insight and recommendations to people and to automatedsystems through any of the predictive analytics applications.

SAS

The SAS System, originally Statistical Analysis System, is an integrated system ofsoftware products provided by SAS Institute that enables the programmer to perform:

· Data entry, retrieval, management, and mining· Report writing and graphics· Statistical and mathematical analysis· Business planning, forecasting, and decision support· Operations research and project management· Quality improvement· Applications development· Warehousing (extract, transform, load}· Platform independent and remote computing

In addition, the SAS System integrates with many SAS business solutions that enablelarge scale software solutions for areas such as human resource management, financialmanagement, business intelligence, customer relationship management and more.

Statistical analyses using SPSS

Introduction

This section shows how to perform a number of statistical tests using SPSS. Each sectiongives a brief description of the aim of the statistical test, when it is used, an exampleshowing the SPSS commands and SPSS (often abbreviated} output with a briefinterpretation of the output. In deciding which test is appropriate to use, it is importantto consider the type of variables that you have (i.e., whether your variables arecategorical, ordinal or interval and whether they are normally distributed).

Statistical methods using SPSS

One sample t-test

A one sample t-test allows us to test whether a sample mean (of a normally distributedinterval variable) significantly differs from a hypothesized value. For example, using thedata file, say we wish to test whether the average writing score (write) differssignificantly from 50. We can do this as shown below:

t-test

/testval = 50

/variable = write.

The mean of the variable write for this particular sample of students is 52.775, which isstatistically significantly different from the test value of 50. We would conclude that thisgroup of students has a significantly higher mean on the writing test than 50.

One sample median test

A one sample median test allows us to test whether a sample median differs significantlyfrom a hypothesized value. We will use the same variable, write, as we did in the onesample t-test example above, but we do not need to assume that it is interval andnormally distributed (we only need to assume that write is an ordinal variable).However, we are unaware of how to perform this test in SPSS.

Binomial test

A one sample binomial test allows us to test whether the proportion of successes on atwo-level categorical dependent variable significantly differs from a hypothesized value.For example, using the, say we wish to test whether the proportion of females (female)differs significantly from 50%, i.e., from 0.5. We can do this as shown below:

npar tests

/binomial (.5) = female.

a. Based on Z Approximation.

The results indicate that there is no statistically significant difference (p =0.229). Inother words, the proportion of females in this sample does not significantly differ fromthe hypothesized value of 50%.

Chi-square goodness of fit

A chi-square goodness of fit test allows us to test whether the observed proportions for acategorical variable differ from hypothesized proportions. For example, let's supposethat we believe that the general population consists of 10% Hispanic, 10% Asian, 10%African American and 70% White folks. We want to test whether the observedproportions from our sample differ significantly from these hypothesized proportions.

npar test

/chisquare = race

/expected = 10 10 10 70.

a. 0 cells (0%) have expected count less than 5. The minimum expected cell frequency is20.0

These results show that racial composition in our sample does not differ significantlyfrom the hypothesized values that we supplied (chi-square with three degrees offreedom = 5.029, p = 0.170).

Two independent samples t-test

An independent samples t-test is used when you want to compare the means of anormally distributed interval dependent variable for two independent groups. Forexample, using the, say we wish to test whether the mean for write is the same for malesand females.

t-test groups = female(0 1)

/variables = write.

The results indicate that there is a statistically significant difference between the meanwriting score for males and females (t = -3.734, p = 0.000). In other words, femaleshave a statistically significantly higher mean score on writing (54.99) than males(50.12).

Chi-square test

A chi-square test is used when you want to see if there is a relationship between twocategorical variables. In SPSS, the chi2 option is used with the tabulate command toobtain the test statistic and its associated p-value. Let's see if there is a relationshipbetween the type of school attended (schtyp) and student’s gender (female).Remember that the chi-square test assumes that the expected value for each cell is fiveor higher. This assumption is easily met in the examples below. However, if thisassumption' is not met in your data, please see the section on Fisher's exact test below.

a. Computed only for a 2x2 table

b. 0 cells (.0%) have expected count less than 5. The minimum expected count is 14.56.

These results indicate that there is no statistically significant relationship between thetype of school attended and gender (chi-square with one degree of freedom = 0.047, p =0.828).

Let's look at another example, this time looking at the linear relationship betweengender (female) and socio-economic status (ses). The point of this example is that one(or both) variables may have more than two levels, and that the variables do not have tohave the same number of levels. In this example, female has two levels (male andfemale) and ses has three levels (low, medium and high).

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 21.39.

Again we find that there is no statistically significant relationship between the variables(chi-square with two degrees of freedom = 4.577, p = 0.101).

Fisher's exact test

The Fisher's exact test is used when you want to conduct a chi-square test but one ormore of your cells have an expected frequency of five or less. Remember that the chi-square test assumes that each cell has an expected frequency of five or more, but theFisher's exact test has no such assumption and can be used regardless of how small theexpected frequency is. In SPSS unless you have the SPSS Exact Test Module, you canonly perform a Fisher's exact test on a 2x2 table, and these results are presented bydefault. Please see the results from the chi squared example above.

One-way ANOVA

A one-way analysis of variance (ANOVA) is used when you have a categoricalindependent variable (with two or more categories) and a normally distributed intervaldependent variable and you wish to test for differences in the means of the dependentvariable broken down by the levels of the independent variable. For example, using thedata file, say we wish to test whether the mean of write differs between the threeprogram types (prog).

The mean of the dependent variable differs significantly among the levels of programtype. However, we do not know if the difference is between only two of the levels or allthree of the levels. (The F test for the Model is the same as the F test for prog becauseprog was the only variable entered into the model. If other variables had also beenentered, the F test for the Model would have been different from prog). To see themean of write or each level of program type

From this we can see that the students in the academic program have the highest meanwriting score, while students in the vocational program have the lowest.

Discriminant analysis

Discriminant analysis is used when you have one or more normally distributed intervalindependent variables and a categorical dependent variable It is a multivariatetechnique that considers the latent dimensions in the independent variables forpredicting group membership in the categorical dependent variable.

Pooled within-groups correlations between discriminating variables and standardizedcanonical discriminant functions. Variables ordered by absolute size of correlationwithin function.

*Largest absolute correlation between each variable and any discriminant function

Clearly, the SPSS output for this procedure is quite lengthy, and it is beyond the scope ofthis page to explain all of it. However, the main point is that two canonical variables areidentified by the analysis, the first of which seems to be more related to program typethan the second.

Factor analysis

Factor analysis is a form of exploratory multivariate analysis that is used to eitherreduce the number of variables in a model or to detect relationships among variables.All variables involved in the factor analysis need to be interval and are assumed to benormally distributed. The goal of the analysis is to try to identify factors which underliethe variables. There may be fewer factors than variables, but there may not be morefactors than variables. For our example, let's suppose that we think that there are somecommon factors underlying the various test scores. We will include subcommands forvarimax rotation and a plot of the eigenvalues. We will use a principal componentsextraction and will retain two factors. (Using these options will make our resultscompatible with those from SAS and Stata and are not necessarily the options that youwill want to use).

Communality (which is the opposite of uniqueness) is the proportion of variance of thevariable (i.e., read) that is accounted for by all of the factors taken together, and a verylow communality can indicate that a variable may not belong with any of the factors.The screen plot may be useful in determining how many factors to retain. From thecomponent matrix table, we can see that all five of the test scores load onto the firstfactor, while all five tend to load not so heavily on the second factor. The purpose ofrotating the factors is to get the variables to load either very high or very low on eachfactor. In this example, because all of the variables loaded onto factor 1 and not on factor2, the rotation did not aid in the interpretation. Instead, it made the results even moredifficult to interpret.

SUMMARY

The statistical packages applied for the management research process are SPSS, SASand STATA. This software makes the research process effective. It reduces the time ofdoing analysis. Large data also can be easily analyzed using these softwares.

The chapter also given the detailed procedures and interpretation of SPSS output forstatistical tests.

KEY TERMS

· SPSS· SAS· STATA· Dependent variable· Independent variable

REVIEW QUESTIONS

1. Define SPSS

2. What do you mean by STATA and SAS

3. List out the application of statistical software to the market research

4. Define dependent variable

5. Define independent variable

6. Differentiate the relative frequency and cumulative frequency with suitable

- End of Chapter -

LESSON – 20

ADVANCED DATA TECHNIQUES

OBJECTIVES

To understand the procedures and applications of following statistical analysis -

o Discriminant analysiso ANOVAo Multi dimensional Scalingo Cluster analysis

STRUCTURE

· Analysis of variance· Condition for ANOVA· ANOVA model· Discriminant analysis· Factor analysis· Cluster analysis· Ward's method

Analysis of Variance (ANOVA)

Analysis of variance (ANOVA) is used to test hypotheses about differences between twoor more means. The t-test based on the standard error of the difference between two

means can only be used to test differences between two means. When there are morethan two means, it is possible to compare each mean with each other mean using t-tests.However, conducting multiple t-tests can lead to severe inflation of the Type I error rate.Analysis of variance can be used to test differences among several means for significancewithout increasing the Type I error rate. This chapter covers designs with between-subject variables. The next chapter covers designs with within-subject variables.

The statistical method for testing the null hypothesis that the means of severalpopulations are equal is analysis of variance. It uses a single factor, fixed -effects modelto compare the effects of one factor (brands of coffee, varieties if residential housing,types if retail stores) on a continuous dependent variable. In a fixed effects model, thelevels of the factor are established in advance and the results are not generalizable toother levels of treatment.

Consider a hypothetical experiment on the effect of the intensity of distractingbackground noise on reading comprehension. Subjects were randomly assigned to oneof three groups. Subjects in Group 1 were given 30 minutes to read a story without anybackground noise. Subjects in Group 2 read the story with moderate background noise,and subjects in Group 3 read the story in the presence of loud background noise.

The first question the experimenter was interested in was whether background noise hasany effect at all. That is, whether the null hypothesis: μ1 = μ2 = μ3 is true where μ1 is thepopulation mean for the "no noise" condition, μ2 is the population mean for the"moderate noise" condition, and μ3 is the population mean for the "loud noise"condition. The experimental design therefore has one factor (noise intensity) and thisfactor has three levels: no noise, moderate noise, and loud noise.

Analysis of variance can be used to provide a significance test of the null hypothesis thatthese three population means are equal. If the test is significant, then the nullhypothesis can be rejected and it can be concluded that background noise has an effect.

In a one-factor between subjects ANOVA, the letter "a" is used to indicate the number oflevels of the factor (a = 3 for the noise intensity example). The number of subjectsassigned to condition 1 is designated as n1; the number of subjects assigned to condition2 is designated by n2, etc.

If the sample size is the same for all of the treatment groups, then the letter "n" (withouta subscript) is used to indicate the number of subjects in each group. The total numberof subjects across all groups is indicated by "N". If the sample sizes are equal, then N =(a)(n); otherwise,

N = n1 + n2 + ... + na

Some experiments have more than one between-subjects factor. For instance, consider ahypothetical experiment in which two age groups (8-year olds and 12-year olds) areasked to perform a task either with or without distracting background noise. The twofactors are age and distraction.

Assumptions

Analysis of variance assumes normal distributions and homogeneity of variance.Therefore, in a one-factor ANOVA, it is assumed that each of the populations isnormally distributed with the same variance (σ2). In between-subjects analyses, it isassumed that each score is sampled randomly and independently. Research has shownthat ANOVA is "robust" to violations of its assumptions.

This means that the probability values computed in an ANOVA are satisfactorilyaccurate even if the assumptions are violated. Moreover, ANOVA tends to beconservative when its assumptions are violated. This means that although power isdecreased, the probability of a Type I error is as low or lower than it would be if itsassumptions were met. There are exceptions to this rule. For example, a combination ofunequal sample sizes and a violation of the assumption of homogeneity of variance canlead to an inflated Type I error rate.

Conditions for ANOVA

1. The sample must be randomly selected from normal populations

2. The populations should have equal variances

3. The distance from one value to its group's mean should be independent of thedistances of other values to that mean (independence of error).

4. Minor variations from normality and equal variances are tolerable. Nevertheless, theanalyst should check the assumptions with the diagnostic techniques.

Analysis of variance breaks down or partitions total variability into component parts.Unlike the 't' test, which uses the sample standard deviations, ANOVA uses squareddeviations of the variance so computation of distances of the individual data points fromtheir own mean or from the grand mean can be summed.

In ANOVA model, each group has its own mean and values that deviate from that mean.Similarly, all the data points from all of the groups produce an overall grand mean. Thetotal deviation is the sum of the squared differences between each data point and theoverall grand mean.

The total deviation of any particular data point may be partitioned into between-groupsvariance and within-group variance. The between-group variance represents the effectof the treatment or factor. The difference of between-groups means imply that eachgroup was treated differently. The treatment will appear as deviations of the samplemeans from the grand mean. Even if this were not so, there would still be some naturalvariability among subjects and some variability attributable to sampling. The within-groups variance describes the deviations of the data points within each group from thesample mean. This results from variability among subjects and from random variation.It is often called error.

When the variability attributable to the treatment exceeds the variability arising fromerror and random fluctuations, the viability of the null hypothesis begins to diminish.And this is exactly the way the test static for analysis of variance works.

The test statistics for ANOVA is the F ratio. It compares the variance from the last twosources:

To compute the F ratio, the sum of the squared deviations for the numerator anddenominator are divided by their respective degrees of freedom. By dividing, computingthe variances as an average or mean, thus the term mean square. The number of degreesof freedom for the numerator, the mean square between groups, is one less than thenumber of groups (k-1). The degree of freedom for the denominator, the mean squarewithin groups, is the total number of observations minus the number of groups (n-k).

If the null hypothesis is true, there should be no difference between the populations, andthe ratio should be close to 1. If the population means are not equal, the numeratorshould manifest this difference. The F ratio should be greater than 1. The f distributiondetermines the size of ratio necessary to reject the null hypothesis for a particularsample size and level of significance.

ANOVA model

To illustrate reports one way ANOVA, consider the following hypothetical example. Tofind out the number one best business school in India, 20 business magnets wererandomly selected and asked to rate the top 3 B-schools. The ratings are given below:

Data

Let's apply the one way ANOVA test on this example.

Step 1: null hypothesis

H0: μA1 = μA2 = μA3

HA: μA1 ≠ μA2 ≠ μA3

Step 2: statistical test

The F test is chosen because the example has independent samples, accept theassumptions of analysis of variance and have interval data.

Step 3: significance level

Let a = 0.05 and degree of freedom = [numerator (k-1) = (3-1) = 2], [denominator (n-k)= (60-3) = 57] = 2, 57

Step 4: calculated value

F = Mean Square between / Mean square within

F= 5822.017/ 205.695 = 28.304 degree of freedom (2, 57)

Step 5: critical test value

From the F-distribution table with degree of freedom (2, 57), α = 0.05, the critical valueis 3.16.

Step 6: decision

Since the calculated value is greater than the critical value (28.3 > 3.16), the nullhypothesis is rejected. The conclusion is: there is statistically significant differencebetween two or more pairs of means. The following table shows that the p value equals0.0001. Since the p value (0.0001) is less than the significance level (0.05), this is thesecond method for rejecting the null hypothesis.

The ANOVA model summary given in the following table is the standard way ofsummarizing the results of analysis of variance. It contains the sources of variation,degrees of freedom, sum of squares, mean squares and calculated F value. Theprobability of rejecting the null hypothesis is computed up to 100 percent α -- that is,the probability value column reports the exact significance for the F ratio being tested.

S = Significantly different at this level. Significance level: 0.05

All data are hypothetical

Figures on One-way analysis of variance plots

Discriminant analysis

Discriminant function analysis is used to determine which variables discriminatebetween two or more naturally occurring groups. For example, an educationalresearcher may want to investigate which variables discriminate between high schoolgraduates who decide (1) to go to college, (2) to attend a trade or professional school, or(3) to seek no further training or education. For that purpose the researcher couldcollect data on numerous variables prior to students’ graduation. After graduation, moststudents will naturally fall into one of the three categories. Discriminant Analysis couldthen be used to determine which variable(s) are the best predictors of students’subsequent educational choice.

A medical researcher may record different variables relating to patients’ backgrounds inorder to learn which variables best predict whether a patient is likely to recovercompletely (group 1), partially (group 2), or not at all (group 3). A biologist could recorddifferent characteristics of similar types (groups) of flowers, and then perform aDiscriminant function analysis to determine the set of characteristics that allows for thebest discrimination between the types.

Computational Approach

Let us consider a simple example. Suppose we measure height in a random sample of 50males and 50 females. Females are, on the average, not as tall as males, and thisdifference will be reflected in the difference in means (for the variable Height).Therefore, variable height allows us to discriminate between males and females with abetter than chance probability: if a person is tall, it is likely to be a male, if a person isshort, it is likely to be a female.

We can generalize this reasoning to groups and variables that are less "trivial." Forexample, suppose we have two groups of high school graduates: Those who choose toattend college after graduation and those who do not. We could have measured students'stated intention to continue on to college one year prior to graduation. If the means forthe two groups (those who actually went to college and those who did not) are different,then we can say that intention to attend college as stated one year prior to graduationallows us to discriminate between those who are and are not college bound (and thisinformation may be used by career counselors to provide the appropriate guidance tothe respective students).

To summarize the discussion so far, the basic idea underlying discriminant functionanalysis is to determine whether groups differ with regard to the mean of a variable, andthen to use that variable to predict group membership (e.g., of new cases).

Stepwise Discriminant Analysis

Probably the most common application of Discriminant function analysis is to includemany measures in the study, in order to determine the ones that discriminate betweengroups. For example, an educational researcher interested in predicting high schoolgraduates' choices for further education would probably include as many measures of

personality, achievement motivation, academic performance, etc. as possible in order tolearn which one(s) offer the best prediction.

Model. Put another way, we want to build a "model" of how we can best predict towhich group a case belongs. In the following discussion wc will use the term "in themodel" in order to refer to variables that are included in the prediction of groupmembership, and we will refer to variables as being "not in the model" if they are notincluded.

Forward stepwise analysis. In stepwise discriminant function analysis, a model ofdiscrimination is built step-by-step. Specifically, at each step all variables are reviewedand evaluated to determine which one will contribute most to the discriminationbetween groups. That variable will then be included in the model, and the process startsagain.

Backward stepwise analysis. One can also step backwards; in that case allvariables are included in the model and then, at each step, the variable that contributesleast to the prediction of group membership is eliminated. Thus, as the result of asuccessful discriminant function analysis, one would only keep the "important"variables in the model, that is, those variables that contribute the most to thediscrimination between groups.

F to enter, F to remove. The stepwise procedure is "guided" by the respective F toenter and F to remove values. The F value for a variable indicates its statisticalsignificance in the discrimination between groups, that is, it is a measure of the extent towhich a variable makes a unique contribution to the prediction of group membership.

Capitalizing on chance. A common misinterpretation of the results of stepwisediscriminant analysis is to take statistical significance levels at face value. By nature, thestepwise procedures will capitalize on chance because they "pick and choose" thevariables to be included in the model so as to yield maximum discrimination. Thus,when using the stepwise approach the researcher should be aware that the significancelevels do not reflect the true alpha error rate, that is, the probability of erroneouslyrejecting H0 (the null hypothesis that there is no discrimination between groups).

Multi Dimensional Scaling

Multidimensional scaling (MDS) is a set of related statistical techniques often used indata visualisation for exploring similarities or dissimilarities in data. An MDS algorithmstarts with a matrix of item-item similarities, and then assigns a location of each item ina low-dimensional space, suitable for graphing or 3D visualisation.

Categorization of MDS

MDS algorithms fall into a taxonomy, depending on the meaning of the input matrix:

♦ Classical multidimensional scaling also often called Metric multidimensionalscaling -- assumes the input matrix is just an item-item distance matrix. Analogous toPrincipal components analysis, an eigenvector problem is solved to find the locationsthat minimize distortions to the distance matrix. Its goal is to find a Euclidean distanceapproximating a given distance. It can be generalized to handle 3-way distanceproblems (the generalization is known as DISTATIS).

♦ Metric multidimensional scaling -- A superset of classical MDS that assumes aknown parametric relationship between the elements of the item-to-item dissimilaritymatrix and the Euclidean distance between the items.

♦ Generalized multidimensional scaling (GMDS) -- A superset of metric MDSthat allows for the target distances to be non-Euclidean.

♦ Non-metric multidimensional scaling -- In contrast to metric MDS, non-metricMDS both finds a non-parametric monotonic relationship between the dissimilarities inthe item-item matrix and the Euclidean distance between items, and the location of eachitem in the low-dimensional space. The relationship is typically found using isotonicregression.

Multidimensional Scaling Procedure

There are several steps in conducting MDS research:

1. Formulating the problem - What brands do you want to compare? How manybrands do you want to compare? More than 20 would be cumbersome. Less than 8 (4pairs) will not give valid results. What purpose is the study to be used for?

2. Obtaining Input Data - Respondents are asked a series of questions. For eachproduct pair they are asked to rate similarity (usually on a 7 point Likert scale from verysimilar to very dissimilar). The first question could be for Coke/Pepsi for example, thenext for Coke/Hires rootbeer, the next for Pepsi/Dr Pepper, the next for DrPepper/Hires rootbeer, etc. The number of questions is a function of the number ofbrands and can be calculated as Q = N (N - 1) / 2 where Q is the number of questionsand N is the number of brands. This approach is referred to as the "Perception data:direct approach". There are two other approaches. There is the "Perception data:derived approach" in which products are decomposed into attributes which are rated ona semantic differential scale. The other is the "Preference data approach" in whichrespondents are asked their preference rather than similarity.

3. Running the MDS statistical program - Software for running the procedure isavailable in most of the better statistical applications programs. Often there is a choicebetween Metric MDS (which deals with interval or ratio level data), and Non-metricMDS (which deals with ordinal data). The researchers must decide on the number ofdimensions they want the computer to create. The more dimensions, the better thestatistical fit, but the more difficult it is to interpret the results.

4. Mapping the results and defining the dimensions - The statistical program(or a related module) will map the results. The map will plot each product (usually intwo dimensional space). The proximity of products to each other indicates either howsimilar they are or how preferred they are, depending on which approach was used. Thedimensions must be labelled by the researcher. This requires subjective judgment and isoften very challenging. The results must be interpreted.

5. Test the results for reliability and validity - Compute R squared to determinewhat proportion of variance of the scaled data can be accounted for by the MDSprocedure. An R-square of 0.6 is considered the minimum acceptable level. Otherpossible tests are Kruskal's Stress, split data tests, data stability tests (i.e. eliminatingone brand), and test-retest reliability.

Input Data

The input to MDS is a square, symmetric 1-mode matrix indicating relationships amonga set of items. By convention, such matrices are categorized as either similarities ordissimilarities, which are opposite poles of the same continuum. A matrix is a similaritymatrix if larger numbers indicate more similarity between items, rather than less. Amatrix is a dissimilarity matrix if larger numbers indicate less similarity. The distinctionis somewhat misleading, however, because similarity is not the only relationship amongitems that can be measured and analyzed using MDS. Hence, many input matrices areneither similarities nor dissimilarities.

However, the distinction is still used as a means of indicating whether larger numbers inthe input data should mean that a given pair of items should be placed near each otheron the map, or far apart. Calling the data "similarities" indicates a negative ordescending relationship between input values and corresponding map distances, whilecalling the data "dissimilarities" or "distances" indicates a positive or ascendingrelationship.

A typical example of an input matrix is the aggregate proximity matrix derived from apile-sort task. Each cell xij of such a matrix records the number (or proportion) ofrespondents who placed items i and j into the same pile. It is assumed that the numberof respondents placing two items into the same pile is an indicator of the degree towhich they are similar. An MDS map of such data would put items close together whichwere often sorted into the same piles.

Another typical example of an input matrix is a matrix of correlations among variables.Treating these data as similarities (as one normally would), would cause the MDSprogram to put variables with high positive correlations near each other, and variableswith strong negative correlations far apart.

Another type of input matrix is a flow matrix. For example, a dataset might consist ofthe number of business transactions occurring during a given period between a set ofcorporations. Running this data through MDS might reveal clusters of corporations thatwhose members trade more heavily with one another than other than with outsiders.

Although technically neither similarities nor dissimilarities, these data should beclassified as similarities in order to have companies who trade heavily with each othershow up close to each other on the map.

Dimensionality

Normally, MDS is used to provide a visual representation of a complex set ofrelationships that can be scanned at a glance. Since maps on paper are two-dimensionalobjects, this translates technically to finding an optimal configuration of points in 2-dimensional space. However, the best possible configuration in two dimensions may bea very poor, highly distorted, representation of your data. If so, this will be reflected in ahigh stress value. When this happens, you have two choices: you can either abandonMDS as a method of representing your data, or you can increase the number ofdimensions.

There are two difficulties with increasing the number of dimensions:

The first is that even 3 dimensions are difficult to display on paper and aresignificantly more difficult to comprehend. Four or more dimensions render MDSvirtually useless as a method of making complex data more accessible to thehuman mind.

The second problem is that with increasing dimensions, you must estimate anincreasing number of parameters to obtain a decreasing improvement in stress.The result is model of the data that is nearly as complex as the data itself.

On the other hand, there are some applications of MDS for which high dimensionalityare not a problem. For instance, MDS can be viewed as a mathematical operation thatconverts an item-by-item matrix into an item-by-variable matrix. Suppose, for example,that you have a person-by-person matrix of similarities in attitudes. You would like toexplain the pattern of similarities in terms of simple personal characteristics such asage, sex, income and education. The trouble is that these two kinds of data are notconformable. The person-by-person matrix in particular is not the sort of data you canuse in a regression to predict age (or vice-versa). However, if you run the data throughMDS (using very high dimensionality in order to achieve perfect stress), you can create aperson-by-dimension matrix which is similar to the person-by-demographics matrixthat you are trying to compare it to.

MDS and Factor Analysis

Even though there are similarities in the type of research questions to which these twoprocedures can be applied, MDS and factor analysis are fundamentally differentmethods. Factor analysis requires that the underlying data are distributed asmultivariate normal, and that the relationships are linear. MDS imposes no suchrestrictions. As long as the rank-ordering of distances (or similarities) in the matrix ismeaningful, MDS can be used. In terms of resultant differences, factor analysis tends toextract more factors (dimensions) than MDS; as a result, MDS often yields more readily,

interpretable solutions. Most importantly, however, MDS can be applied to any kind ofdistances or similarities, while factor analysis requires us to first compute a correlationmatrix. MDS can be based on subjects' direct assessment of similarities between stimuli,while factor analysis requires subjects to rate those stimuli on some list of attributes (forwhich the factor analysis is performed).

In summary, MDS methods are applicable to a wide variety of research designs becausedistance measures can be obtained in any number of ways.

Applications

Marketing

In marketing, MDS is a statistical technique for taking the preferences and perceptionsof respondents and representing them on a visual grid. These grids, called perceptualmaps, are usually two-dimensional, but they can represent more than two.

Potential customers are asked to compare pairs of products and make judgments abouttheir similarity. Whereas other techniques obtain underlying dimensions fromresponses to product attributes identified by the researcher, MDS obtains theunderlying dimensions from respondents' judgments about the similarity of products.This is an important advantage. It does not depend on researchers' judgments. It doesnot require a list of attributes to be shown to the respondents. The underlyingdimensions come from respondents’ judgments about pairs of products. Because ofthese advantages, MDS is the most common technique used in perceptual mapping.

The "beauty" of MDS is that we can analyze any kind of distance or similarity matrix.These similarities can represent people's ratings of similarities between objects, thepercent agreement between judges, the number of times a subjects fails to discriminatebetween stimuli, etc. For example, MDS methods used to be very popular inpsychological research on person perception where similarities between trait descriptorswere analyzed to uncover the underlying dimensionality of people's perceptions of traits(see, for example Rosenberg, 1977). They are also very popular in marketing research, inorder to detect the number and nature of dimensions underlying the perceptions ofdifferent brands or products & Carmone, 1970).

In general, MDS methods allow the researcher to ask relatively unobtrusive questions("how similar is brand A to brand B") and to derive from those questions underlyingdimensions without the respondents ever knowing what is the researcher's real interest.

Cluster Analysis

The term cluster analysis (first used by Tryon, 1939) encompasses a number of differentalgorithms and methods for grouping objects of similar kind into respective categories.A general question facing researchers in many areas of inquiry is how to organizeobserved data into meaningful structures, that is, to develop taxonomies. In other wordscluster analysis is an exploratory data analysis tool which aims at sorting different

objects into groups in a way that the degree of association between two objects ismaximal if they belong to the same group and minimal otherwise. Given the above,cluster analysis can be used to discover structures in data without providing anexplanation/interpretation. In other words, cluster analysis simply discovers structuresin data without explaining why they exist.

We deal with clustering in almost every aspect of daily life. For example, a group ofdiners sharing the same table in a restaurant may be regarded as a cluster of people. Infood stores items of similar nature, such as different types of meat or vegetables aredisplayed in the same or nearby locations. There is countless number of examples inwhich clustering plays an important role. For instance, biologists have to organize thedifferent species of animals before a meaningful description of the differences betweenanimals is possible. According to the modern system employed in biology, man belongsto the primates, the mammals, the amniotes, the vertebrates, and the animals. Note howin this classification, the higher the level of aggregation the less similar are the membersin the respective class. Man has more in common with all other primates (e.g., apes)than it does with the more "distant" members of the mammals (e.g., dogs), etc. For areview of the general categories of cluster analysis methods, see Joining (TreeClustering), Two-way Joining (Block Clustering), and k-Means Clustering.

Cluster Analysis (CA) is a classification method that is used to arrange a set of cases intoclusters. The aim is to establish a set of clusters such that cases within a cluster are moresimilar to each other than they are to cases in other clusters.

Cluster analysis is an exploratory data analysis tool for solving classification problems.Its object is to sort cases (people, things, events, etc) into groups, or clusters, so that thedegree of association is strong between members of the same cluster and weak betweenmembers of different clusters. Each cluster thus describes, in terms of the data collected,the class to which its members belong; and this description may be abstracted throughuse from the particular to the general class or type.

Cluster analysis is thus a tool of discovery. It may reveal associations and structure indata which, though not previously evident, nevertheless are sensible and useful oncefound. The results of cluster analysis may contribute to the definition of a formalclassification scheme, such as taxonomy for related animals, insects or plants; or suggeststatistical models with which to describe populations; or indicate rules for assigning newcases to classes for identification and diagnostic purposes; or provide measures ofdefinition, size and change in what previously were only broad concepts; or findexemplars to represent classes.

Whatever business you're in, the chances are that sooner or later you will run into aclassification problem. Cluster analysis might provide the methodology to help yousolve.

Procedure for Cluster Analysis

1. Formulate the problem - select the variables that you wish to apply the clusteringtechnique to

2. Select a distance measure - various ways of computing distance:

· Squared Euclidean distance - the square root of the sum of the squareddifferences in value for each variable

· Manhattan distance - the sum of the absolute differences in value for any variable· Chebychev distance - the maximum absolute difference in values for any variable

3. Select a clustering procedure (see below)

4. Decide on the number of clusters

5. Map and interpret clusters - draw conclusions - illustrative techniques like perceptualmaps, icicle plots, and dendrograms are useful

6. Assess reliability and validity - various methods:

· repeat analysis but use different distance measure· repeat analysis but use different clustering technique· split the data randomly into two halves and analyze each part separately· repeat analysis several times, deleting one variable each time· repeat analysis several times, using a different order each time

Figure showing three pairs of clusters:

♦ (AB)

♦ (DE)

♦ (FG)

Beyond these we can see that (AB) & (C) and (DE) are more similar to each other than to(FG).

Hence we could construct the following dendrogram (hierarchical classification).

Note that the clusters are joined (fused) at increasing levels of 'dissimilarity'.

The actual measure of dissimilarity will depend upon the method used. It may be asimilarity measure or a distance measure. Distances between points can be calculated byusing an extension of Pythagorus (these are euclidean distances). These measures of'dissimilarity' can be extended to more than 2 variables (dimensions) without difficulty.

Clustering Algorithms

Having selected how we will measure similarity (the distance measure) we must nowchoose the clustering algorithm, i.e. the rules which govern between which pointsdistances are measured to determine cluster membership. There are many methodsavailable, the criteria used differ and hence different classifications may be obtained forthe same data. This is important since it tells us that although cluster analysis mayprovide an objective method for the clustering of cases there can be subjectivity in thechoice of method. Five algorithms, available within SPSS, are described.

1. Average Linkage Clustering2. Complete Linkage Clustering3. Single Linkage Clustering4. Within Groups Clustering5. Ward's Method

1. Average Linkage Clustering

The dissimilarity between clusters is calculated using cluster average values; of coursethere are many ways of calculating an average. The most common (and recommended ifthere is no reason for using other methods) is UPGMA - Unweighted Pair Groups

Method Average. SPSS also provides two other methods based on averages,CENTROID and MEDIAN. Centroid or UPGMC (Unweighted Pair Groups MethodCentroid) uses the group centroid as the average. The centroid is defined as the centre ofa cloud of points. A problem with the centroid method is that some switching andreversal may take place, for example as the agglomeration proceeds some cases mayneed to be switched from their original clusters.

2. Complete Linkage Clustering (Maximum or furthest-neighbour method):The dissimilarity between two groups is equal to the greatest dissimilarity between amember of cluster i and a member of cluster j. This method tends to produce very tightclusters of similar cases.

3. Single Linkage Clustering (Minimum or nearest-neighbour method): Thedissimilarities between two clusters is the minimum dissimilarity between membersof the two clusters. This method produces long chains which form loose, stragglyclusters. This method has been widely used in numerical taxonomy.

4. Within Groups Clustering

This is similar to UPGMA except clusters are fused so that within cluster variance isminimized. This tends to produce tighter clusters than the UPGMA method.

5. Ward's Method

Cluster membership is assessed by calculating the total sum of squared deviations fromthe mean of a cluster. The criterion for fusion is that it should produce the smallestpossible increase in the error sum of squares.

Cluster analysis is the statistical method of partitioning a sample into homogeneousclasses to produce an operational classification. Such a classification may help:

· Formulate hypotheses concerning the origin of the sample, e.g. in evolutionstudies

· Describe a sample in terms of a typology, e.g. for market analysis oradministrative purposes

· Predict the future behaviour of population types. e.g. in modeling economicprospects for different industry sectors

· Optimize functional processes, e.g. business site locations or product design· Assist in identification, e.g. in diagnosing diseases· Measure the different effects of treatments on classes within the population, e.g.

with analysis of variance

SUMMARY

The complete process of generalized hierarchical clustering can be summarized asfollows:

1. Calculate the distance between all initial clusters. In most analyses initial clusters willbe made up of individual cases.

2. Fuse the two most similar clusters and recalculate the distances.

3. Repeat step 2 until all cases are in one cluster.

One of the biggest problems with this Cluster Analysis is identifying the optimumnumber of clusters. As the fusion process continues increasingly dissimilar clustersmust be fused, i.e. the classification becomes increasingly artificial. Deciding upon theoptimum number of clusters is largely subjective, although looking at a graph of thelevel of similarity at fusion versus number of clusters may help. There will be suddenjumps in the level of similarity as dissimilar groups are fused.

KEY TERMS

· SPSS· Tabulation· Cross-tabulation· ANOVA· Discriminant analysis· Factor analysis· Conjoint analysis· MDS· Cluster analysis

REVIEW QUESTIONS

1. What do you mean by cross-tabulation?

2. Write short notes on statistical packages

3. Explain the step wise procedure for doing Discriminant Analysis.

4. Write short notes on ANOVA.

5. Explain the application of Factor analysis in Marketing.

6. What do you mean by conjoint analysis?

7. Explain the procedure of performing Multi Dimensional Scaling.

8. What are the applications of MDS?

9. Describe the different types of cluster analysis.

10. Explain the marketing situations in which the above said tools will be used.

- End of Chapter -

LESSON – 21

FACTOR ANALYSIS

OBJECTIVES

· To learn the basic concepts of Factor.· To understand procedures of performing Factor.· To identify the applications of factor.

STRUCTURE

· Evaluation of factor analysis· Steps involved in conducting the factor analysis· Process involved in factor analysis· Output of factor analysis· Limitation of factor analysis

INTRODUCTION

Factor analysis is a general name denoting a class of procedures primarily used for datareduction and summarization. In marketing research, there may be a large number ofvariables, most of which are correlated and which must be reduced to a manageablelevel. Relationships among sets of many interrelated variables are examined andrepresented in terms of a few underlying factors. For example, store image may bemeasured by asking respondents to evaluate stores on a series of items on a semantic

differential scale. The item evaluations may then be analyzed to determine the factorsunderlying store image.

In analysis of variance, multiple regression, and discriminant analysis, one variable isconsidered as the dependent or criterion variable, and the others as independent orpredictor variables. However, no such distinction is made in factor analysis. Rather,factor analysis is an interdependence technique in that an entire set ofinterdependent relationships is examined.

Factor analysis is used in the following circumstances:

- To identify underlying dimensions, or factors that explain the correlations among a setof variables. For example, a set of lifestyle statements may be used to measure thepsychographic profiles of consumers. These statements may then be factor analyzed toidentify) the underlying psychographic factors, as illustrated in the department storeexample.

- To identify a new, smaller set of uncorrelated variables to replace the original set ofcorrelated variables in subsequent multivariate analysis (regression or discriminantanalysis). For example, the psychographic factors identified may be used as independentvariables to explaining the differences between loyal and non loyal consumers.

- To identify a smaller set of salient variables from a larger set for use in subsequentmultivariate analysis. For example, a few of the original lifestyle statements thatcorrelate highly with the identified factors may be used as independent variables toexplain the differences between the loyal and non-loyal users.

Definition

Factor analysis is a class of procedures primarily used for data reduction andsummarization. Factors analysis is an interdependence technique in that an entire set ofinterdependent relationships is examined. Factors are defined as an underlyingdimension that explains the correlation among a set of variables

Evolution of Factor Analysis

Charles Spearman first used the factor analysis as a technique of indirect measurement.When they test human personality and intelligence, a set of questions and tests aredeveloped for this purpose. They believe that a person gives this set of questions andtests would respond on the basis of some structure that exists in his mind. Thus, hisresponses would form a certain pattern. This approach is based on the assumption thatthe underlying structure in answering the questions would be the same in the case ofdifferent respondents.

Even though it is in the field of psychology that factor analysis has its beginning, it hassince been applied to problems in different areas including marketing. Its use has

become far more frequent as a result of the introduction Specialized software packagessuch as SPSS, SAS.

Application of Factor Analysis

· It can be used in market segmentation for identifying the underlying variables onwhich to group the customers. New-car buyers might be grouped based on therelative emphasis place on economy, convenience, performance, comfort, andluxury. This might result in five segments: economy seekers, convenienceseekers, performance seekers, fort seekers, and luxury seekers.

· In product research, factor analysis can be employed to determine the brandattributes that influence consumer choice. Toothpaste brand-might be evaluatedin terms of protection against cavities, whiteness of teeth, taste, fresh breath, andprice.

· In advertising studies, factor analysis can be used to understand the mediaconsumption habits of the target market. The users of frozen foods may be heavyviewers of cable TV, see a lot at movies, and listen to country music.

· In pricing studies, it can be used to identify the characteristics of price-sensitiveconsumers. For example, these consumers might be methodical, economyminded, and home centered.

It can bring out the hidden or latent dimensions relevant in the relationships amongproduct preferences. Factor analysis is typically used to study a complex product orservice in order to identify the major characteristics (or factors) considered to beimportant by consumers of the product or service Example: Researchers for anautomobile (two wheeler) company may ask a large sample of potential buyers to report(using rating scales) the extent of their agreement or disagreement with the number ofstatements such as "A motor bike’s breaks are its most crucial part", "Seats should becomfortable for two members". Researchers apply factor analysis to such a set of data toidentity, which factors such as "safety", "exterior styling", "economy of operations" areconsidered important by potential customers. If this information is available, it can beused to guide the overall characteristics to be designed into the product or to identifyadvertising themes that potential buyers aid consider important.

Steps Involved In Conducting the Factor Analysis:

Statistics Associated with Factor Analysis

The key statistics associated with factor analysis are as follows:

» Bartlett's test of sphericity: A test statistic used to examine the hypothesis that thevariables are uncorrelated in the population. In other words, the population correlationmatrix is an identity matrix; each variable correlates perfectly with itself (r = 1) but hasno correlation with the other variables (r = 0).

» Correlation matrix: A lower triangle matrix showing the simple correlations, r,between all possible pairs of variables included in the analysis. The diagonal elements,which are all I, are usually omitted.

» Communality: The amount of variance a variable shares with all the other variablesbeing considered. This is also the proportion of variance explained by the commonfactors.

» Eigenvalue: Represents the total variance explained by each factor.

» Factor loadings: Simple correlations between the variables and the factors.

» Factor loading plot: A plot of the original variables using the factor loadings ascoordinates.

» Factor matrix: Contains the factor loadings of all the variables on all the factorsextracted.

» Factor scores: Composite scores estimated for each respondent on the derivedfactors.

» Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy. An index used toexamine the appropriateness of factor analysis. High values (between 0.5 and 1.0)indicate factor analysis is appropriate. Values below 0.5 imply that factor analysis maynot be appropriate.

» Percentage of variance: The percentage of the total variance attributed to eachfactor.

» Residuals: The differences between the observed correlations, as given in the inputcorrelation matrix, and the reproduced correlations, as estimated from the factormatrix.

» Scree plot: A plot of the eigenvalues against the number of factors in order ofextraction. We describe the uses of these statistics in the next section, in the context ofthe procedure for conducting factor analysis.

Process Involved In Factor Analysis

Factor analysis applies an advanced form of correlation analysis to the responses tonumber of statements. The purpose of this analysis is to determine if the responses toseveral of statements are highly correlated .If the responses to three or more statementsare highly correlated, it is believed that the statements measure some factor common toall of them.

The statements in any one set are highly correlated with each other but are not highlycorrelated with the statements in any of the other sets.

For each set of highly correlated statements, the researchers use their own judgment todetermine what the single "theme" or "factor" is that ties the statements together in theminds of the respondents. For example, regarding the automobile study mentionedabove, researchers may find high correlations among the responses to the followingthree statements:

i. Mileage per liter should be high; ii. Maintenance cost should be low; iii. Mileageshould be consistent in all types of roads.

The researcher may then make the judgment that agreement with these set ofstatements indicates an underlying concern with the factor of "Economy of operation".

Determine the Method of Factor Analysis

Once it has been determined that factor analysis is an appropriate technique foranalyzing data, an appropriate method must be selected. The approach used to derivethe weights factor score coefficients differentiates the various methods of factor analysis.The two basic approaches are principal components analysis and common factoranalysis. In principal components analysis, the total variance in the data is considered.The diagonal of correlation matrix consists of unities, and full variance is brought intothe factor matrix. Principal components analysis is recommended when theprimary concern is to determine the minimum number of factors that will account formaximum variance in the data for use in subsequent multivariate analysis. The factorsare called principal components.

In common factor analysis, the factors are estimated based only on the commonvariance. Communalities are inserted in the diagonal of the correlation matrix. Thismethod is appropriate when the primary concern is to identify the underlyingdimensions and the common variance is of interest. This method is also known asprincipal axis factoring.

Other approaches for estimating the common factors are also available. These includemethods of unweighted least squares, generalized least squares, maximum likelihood,HA method, and image factoring. These methods are complex and are notrecommended for experienced users.

Determine the Number of Factors

It is possible to compute as many principal components as there are variables, but indoing so, no parsimony is gained. In order to summarize the information contained inthe original variables, a smaller number of factors should be extracted. The question is,how many? Several procedures have been suggested for determining the number offactors. These include a priori determination and approaches based on eigenvalues,scree plot, percentage variance accounted for, split-half reliability, and significancetests.

A Prior Determination. Sometimes, because of prior knowledge, the researcherknows many factors to expect and thus can specify the number of factors to be extractedbeforehand. The extraction of factors ceases when the desired number of factors havebeen extracted. Most computer programs allow the user to specify the number offactors, allowing for an easy implementation of this approach.

Determination Based on Eigenvalues. In this approach, only factors witheigenvalues greater than 1.0 are retained; the other factors are not included in themodel. An eigenvalue sends the amount of variance associated with the factor. Hence,only factors with a variance greater than 1.0 are included. Factors with variance lessthan 1.0 are no better than a single variable, because, due to standardization, eachvariable has a variance of 1.0. If the number of variables is less than 20, this approachwill result in a conservative number of factors.

Determination Based on Scree Plot. A scree plot is a plot of the eigenvaluesagainst the number of factors in order of extraction. The shape of the plot is used todetermine the number of factors. Typically, the plot has a distinct break between thesteep slope of factors with large eigenvalues and a gradual trailing off associated withthe rest of the factors. This gradual trailing off is referred to as the scree. Experimentalevidence indicates that point at which the scree begins denotes the true number offactors. Generally, the number of factors determined by a scree plot will be one or a fewmore than that determined by the eigenvalue criterion.

Determination Based on Percentage of Variance. In this approach the numberof factors extracted is determined so that the cumulative percentage of varianceextracted by the factors reaches a satisfactory level. What level of variance is satisfactorydepends upon the problem. However, it is recommended that the factors extractedshould account for at least o percent of the variance.

Determination Based on Split-Half Reliability. The sample is split in half andfactor analysis is performed on each half. Only factors with high correspondence offactor loadings across the two subsamples are retained.

Determination Based on Significance Tests. It is possible to determine theStatistical significance of the separate eigenvalues and retain only those factors that arestatistically, significant. A drawback is that with large samples (size greater than 200),many factors likely to be statistically significant, although from a practical viewpointmany of the count for only a small proportion of the total variance.

Illustration

A manufacturer of motorcycles wanted to know which motorcycle characteristics wereconsidered very important by the customers. The company identified 100 statementsthat related to all characteristics of motorcycles that they believed important. 300potential customers of motorcycles were selected on a probability basis and were askedto rate the 100 statements, five of which are listed below. They were then asked to reporton a 5-point scale the extent to which they agreed or disagreed with the statement.

· Breaks are the most important parts for motorcycles.· Appearance of motorcycle should be masculine· Mileage per liter should be high· Maintenance cost should be low· Mileage should be consistent in all types of roads.

This resulted in a set of data in which each of 300 individuals gave a response to each of100 statements. For any given statement, some individuals were found to agree strongly,some were found to disagree slightly, some neither agreed nor disagreed with thestatement, and so on. Thus, for each statement, there was a distribution of 300responses on a 5-point scale.

Three Important Measures

There are three important measures used in the factor analysis:

1. Variance

2. Standardized scores of an individual's responses

3. Correlation coefficient.

1. Variance

A factor analysis is somewhat like regression analysis in that it tries to "best fit" factorsto a scatter diagram of the data in such a way that the factors explain the varianceassociated with the responses to each statement.

2. Standardized Scores of an Individual's Responses

To facilitate comparisons of the responses from such different scales, researchersstandardize all of the answers from all of the respondents on all statements andquestions.

Thus, an individual's standardized score is nothing more than an actual responsemeasured in terms of the number of standard deviations (+ or -1) it lies away from themean. Therefore, each standardized score is likely to be a value somewhere in the rangeof +3.00 and -3.00, with +3.00 typically being equated to the "agree very strongly"response and -3.00 typically being equated to the "disagree very strongly" response.

3. Correlation Coefficient

The third measure used is the correlation coefficient associated with the standardizedscores of the responses to each pair of statements. The matrix of correlation coefficientsis very important part of factor analysis.

The factor analysis searches through a large set of data to locate two or more sets ofstatements, which have highly correlated responses. The responses to the statements in

one set will all be highly correlated with each other, but they will also be quiteuncorrelated with the responses to the statements in other sets. Since the different setsof statements are relatively uncorrelated with each other, a separate and distinct factorrelative to motorcycles is associated with each set.

It is already noted that Variance is one of the three important measures used in factoranalysis with standardized responses to each statement used in the study.

Factor analysis selects one factor at a time using procedures that "best fit" each other tothe data. The first factor selected is one that fits the data in such a way that it explainsmore of the variance in the entire set of standardized scores than any other possiblefactor. Each factor selected after the first factor must be uncorrelated with the factorsalready selected. This process continues until the procedures cannot find additionalfactors that significantly reduce the unexplained variance in the standardized scores

Output of Factor Analysis

Here, only following six statements (or variables) for simplicity will be used to explainthe output of a factor analysis

XI - Mileage per liter should be high

X2 = Maintenance cost should be low

X3 = Mileage should be consistent in all types of roads.

X4 = Appearance of motorcycle should be masculine

X5 = multiple colors should be available

X6 = Breaks are the most important parts for motorcycles

The results a factor analysis of these six statements will appear in the form shown m thefollowing table which can be used to illustrate the three important outputs from a factoranalysis and how they can be of use to researchers.

Table 1: Factor Analysis Output of the Motorcycle Study

Factor Loadings

The top six rows of the table are associated with the six statements listed above. Thetable shows that the factor analysis has identified three factors (F1, F2 and F3) and thefirst three columns are associated with those factors. For example' the first factor can bewritten as

F1= 0.86 x 1+ 0.84 x 2 + 0.68 x 3 + 0.10 x 4 + 0.06 x 5 + 0.12 x 6

The 18 numbers located in the six rows and three columns are called as factor loadingsand they are one of the 3 useful outputs obtained from a factor analysis. As shown intable, each statement has a factor loading associated with a specific factor and a specificstatement is simply the correlation between that factor and that statementsstandardized response scores.

Thus, table 1 shows that factor 1 is highly correlated with the responses to statement 1(0.86 correlation) and also with the response to statement 2 (0.84 correlation).

Table 1 shows that statements 1 and 2 are not highly correlated (0.12 and 0.18respectively) with factor 2. Thus a factor loading is a measure of how well the factor"fits" the standardized responses to Statement.

Naming the Factors

From the table, it is clear that factor F1 is good fit on the data from statements 1, 2 and3, but a poor fit on the other statements. This indicates that statements 1, 2 and 3 areprobably measuring the same basic attitude or value system; and it is this finding thatprovides the researchers with evidence that factor exists.

By using the knowledge on the industry and the contents of statements 1, 2, and 3researchers from Motorcycle Company subjectively concluded from these results that"Economy of operation" was the factor that tied these statements together in the mindsof the respondents.

Researchers next want to know if the 300 respondents participating in the study mostlyagreed with or disagreed with statements 1, 2 and 3. To answer this question, theresearchers had to look at the 300 standardized responses to each of the statements 1, 2and 3. They found that the means of these responses to each of statements 1, 2 and 3.They found that the means of these responses were +0.97, + 1.32, and +1.18,respectively, for statements 1, 2 and 3, indicating that most respondents agreed with thethree statements as per above discussion on "standardized scores". Since a majority ofrespondents had agreed with these statements, the researchers also concluded that thefactor of "economy of operation" was important in the minds of potential motorcyclecustomers.

Table also shows that F2 is good fit on statements 4 and 5 but a poor fit on the otherstatements. This factor is clearly measuring something different from statements 1, 2, 3and 6. Factor F3 is good fit only on statement 6 and so it is clearly measuring somethingnot being statements 1 to 5. Researchers again subjectively concluded that the factorunderlying statements 4 and 5 was "Comfort" and that statement 6 was related to"safety".

Fit between Data and Factor

Researcher has to find how well all of the identified factors fit the data obtained from allof the respondents on any given statement. Communalities for each statement indicatethe proportion of the variance in the responses to the statement which is explained bythe three identified factors.

For example, Three factors explain 0.89 (89%) of the variance in all of the responses tostatement 5, but only 0.54 (54%) of the variance in all of the responses to statement 3. Itshows that three factors explain 75% or more of the variance associated with statements1, 2, 4, 5 and 6, but only about half of statement 3's variance .Researchers can use thesecommunalities to make a judgment about for most of the variance associated with eachof the six statements in this example, the three factors fit the data quite well.

How well any given factor fits the data from all of the respondents on all of thestatements can be determined by eigenvalue. There is an eigenvalue associated witheach of the factors.

When a factor's eigenvalue is divided by the number of statements used in factoranalysis the resulting figure is the proportion of the variance in the entire set ofstandardized response scores which is explained by that factor i.e. each eigenvalue isdivided by 6 – the number of statements. For example factor F1 explains 0.3226 (32%)of the variance of the standardized response scores from all of the respondents on all sixstatements. By adding these figures for the three factors, three factors together explain

0.3226+0.3090+0.1391 = 0.7707 (77.07%) of the variance in the entire set of responsedata. This figure can be used as a measure of how well, over all, the identified factors fitthe data. In general, a factor analysis that accounts for 60-70% or more of the totalvariance can be considered a good fit to the data.

Limitations

The utility of this technique largely depends to a large extent on the judgment of theresearcher. He has to make number of decisions as to how the factor analysis will comeout. Even with a given set of decisions, different results will emerge from differentgroups of respondents, different mixes of data as also different ways of getting data. Inother words, factor analysis is unable to give a unique solution or result.

As any other method of analysis, a factor analysis will be of little use if the appropriatevariable has not been measured, or if the measurements are inaccurate, or if therelationships in the data are non linear

In the view of ongoing limitations, the exploratory nature of factor analysis becomesclear. As Thurston mentions, the use of factor analysis should not be made wherefundamental and fruitful concepts are already well formulated and tested. It may beused especially in those domains where basic and fruitful concepts are essentiallylacking and where crucial experiments have been difficult to conceive.

SUMMARY

This chapter has overview of factor analysis in detail. Factor analysis is used to findlatent variable or factor among observed variables. With factor analysis you can producea small number of factors frame large number of variables. The induced factor can alsobe used for further analysis.

KEY WORDS

· Factor analysis· Communalities· Factor loading· Correlation matrix· Eigen value

IMPORTANT QUESTIONS

1. What are the applications of factor analysis?

2. What is the significance of factor loading in factor analysis?

3. What do you mean by Eigen value?

- End of Chapter -

LESSON – 22

CONJOINT ANALYSIS

STRUCTURE

· Conjoint analysis· Basics of conjoint analysis· Steps involved in conjoint analysis· Application of conjoint analysis

Conjoint analysis, also called multi attribute compositional models, is a statisticaltechnique that originated in mathematical psychology and was developed by marketingprofessor Paul Green at the Wharton School of the University of Pennsylvania. Today itis used in many of the social sciences and applied sciences including marketing, productmanagement, and operations research. The objective of conjoint analysis is to determinewhat combination of a limited number of attributes is most preferred by respondents. Itis used frequently in testing customer acceptance of new product designs and assessingthe appeal of advertisements. It has been used in product positioning, but there aresome problems with this application of the technique. Recently, new alternatives such asGenetic Algorithms have been used in market research.

The Basics of Conjoint Analysis

The basics of conjoint analysis are easy to understand. It should only take about 20minutes to introduce this topic so you can appreciate what conjoint analysis has to offer.

In order to understand conjoint analysis, let's look at a simple example. Suppose youwanted to book an airline flight and you had a choice of spending Rs.400 or Rs.700 for aticket. If this were the only consideration then the choice is clear: the lower priced ticketis preferable. What if the only consideration in booking a flight was sitting in a regularor extra-wide seat? If seat size was the only consideration then you would probablyprefer an extra-wide seat. Finally, suppose you can take either a direct flight which takesthree hours or a flight that stops once and takes five hours. Virtually everyone wouldprefer the direct flight.

Conjoint analysis attempts to determine the relative importance consumers attach tosalient attributes and the utilities they attach to the levels of attributes. This informationis derived from consumers' evaluations of brands, or brand profiles composed of theseattributes and their levels. The respondents are presented with stimuli that consist ofcombinations of attribute levels. They are asked to evaluate these stimuli in terms of

their desirability. Conjoint procedures attempt to assign values to the levels of eachattribute, so that the resulting values or utilities attached to the stimuli match, as closelyas possible the input evaluations provided by the respondents. The underlyingassumption is that any set of stimuli, such as products, brands, or stores, is evaluated asa bundle of attributes.

Conjoint Analysis is a technique that attempts to determine the relative importanceconsumers attach to salient attributes and the utilities they attach to the levels ofattributes.

In a real purchase situation, however, consumers do not make choices based on a singleattribute like comfort. Consumers examine a range of features or attributes and thenmake judgments or trade-offs to determine their final purchase choice. Conjoint analysisexamines these trade-offs to determine the combination of attributes that will be mostsatisfying to the consumer, in other words, by using conjoint analysis a company candetermine the optimal features for their product or service. In addition, conjointanalysis will identify the best advertising message by identifying the features that aremost important in product choice.

Like multidimensional scaling, conjoint analysis relies on respondents' subjectiveevaluations. However, in MDS the stimuli are products or brands. In conjoint analysis,the stimuli are combinations of attribute levels determined by the researcher. The goalin MDS is to develop a spatial map depicting the stimuli in a multidimensionalperceptual or preference space. Conjoint analysis, on the other hand, seeks to developthe part-worth or utility functions describing the utility consumers attach to the levels ofeach attribute. The two techniques are complementary.

In sum, the value of conjoint analysis is that it predicts what products or services peoplewill choose and assesses the weight people give to various factors that underlie theirdecisions. As such, it is one of the most powerful, versatile and strategically importantresearch techniques available.

Statistics and Terms Associated with Conjoint Analysis

The important statistics and terms associated with conjoint analysis include:

· Part-worth functions. Also called utility functions, these describe the utilityconsumers attach to the levels of each attribute.

· Relative importance weights. Indicate which attributes are important ininfluencing consumer choice. These weights are estimated.

· Attribute levels. Denote the values assumed by the attributes.· Full profiles. Full profiles or complete profiles of brands are constructed in

terms of all the attributes by using the attribute levels specified by the design.· Pair-wise tables. The respondents evaluate two attributes at a time until all

the required pairs of attributes have been evaluated.· Cyclical designs. Designs employed to reduce the number of paired

comparisons.

· Fractional factorial designs: Designs employed to reduce the number ofstimulus profiles to be evaluated in the full-profile approach.

· Orthogonal arrays. A special class of fractional designs that enable theefficient estimation of all main effects.

· Internal validity: This involves correlations of the predicted evaluations forthe holdout or validation stimuli with those obtained from the respondents.

Conducting Conjoint Analysis

The following chart lists the steps in conjoint analysis. Formulating the probleminvolves identifying the salient attributes and their levels. These attributes and levels areused for constructing the stimuli to be used in a conjoint evaluation task.

Formulate the Problem

↓

Construct the Stimuli

↓

Decide on the Form of Input Data

↓

Select a Conjoint Analysis Procedure

↓

Interpret the Results

↓

Assess Reliability and Validity

Steps involved in conjoint analysis

The basic steps are:

· Select features to be tested· Show product feature combinations to potential customers· Respondents rank, rate, or choose between the combinations

· Input the data from a representative sample of potential customers into astatistical software program and choose the conjoint analysis procedure. Thesoftware will produce utility functions for each of the features.

· lncorporate the most preferred features into a new product or advertisement.

Any number of algorithms may be used to estimate utility functions. The originalmethods were monotonic analysis of variance or linear programming techniques, butthese are largely obsolete in contemporary marketing research practice. Far morepopular are the Hierarchical Bayesian procedures that operate on choice data. Theseutility functions indicate the perceived value of the feature and how sensitive consumerperceptions and preferences are to changes in product features.

A Practical Example of Conjoint Analysis

Conjoint analysis presents choice alternatives between products/services defined by setsof attributes. This is illustrated by the following choice: would you prefer a flight withregular seats, that costs Rs.400 and takes 5 hours, or a flight which costs Rs.700, hasextra-wide seats and takes 3 hours?

Extending this, we see that if seat comfort, price and duration are the only relevantattributes, there are potentially eight flight choices.

Given the above alternatives, product 4 is very likely the most preferred choice, whileproduct 5 is probably the least preferred product. The preference for the other choices isdetermined by what is important to that individual.

Conjoint analysis can be used to determine the relative importance of each attribute,attribute level, and combinations of attributes. If the most preferable product is notfeasible for some reason (perhaps the airline simply cannot provide extra-wide seats anda 3 hour arrival time at a price of Rs400) then the conjoint analysis will identify the nextmost preferred alternative. If you have other information on travelers, such asbackground demographics, you might be able to identify market segments for which

distinct products may be appealing. For example, the business traveller and the vacationtraveller may have very different preferences which could be met by distinct flightofferings.

You can now see the value of conjoint analysis. Conjoint analysis allows the researcherto examine the trade-offs that people make in purchasing a product. This allows theresearcher to design products/services that will be most appealing to a specific market.In addition, because conjoint analysis identifies important attributes, it can be used tocreate advertising messages that will be most persuasive.

In evaluating products, consumers will always make trade-offs. A traveller may like thecomfort and arrival time of a particular flight, but reject purchase due to the cost. In thiscase, cost has a high utility value. Utility can be defined as a number which representsthe value that consumers place on an attribute. In other words, it represents the relative"worth" of the attribute. A low utility indicates less value; a high utility indicates morevalue.

The following figure presents a list of hypothetical utilities for an individual consumer:

Based on these utilities, we can make the following conclusions:

· This consumer places a greater value on a 3 hour flight (the utility is 42) than ona 5 hour flight (utility is 22).

· This consumer does not differ much in the value that he or she places on comfort.That is, the utilities are quite close (12 vs.15).

· This consumer places a much higher value on a price of Rs.400 than a price ofRs.700.

· The preceding example depicts an individual's utilities. Average utilities can becalculated for all consumers or for specific subgroups of consumers.

These utilities also tell us the extent to which each of these attributes drives the decisionto choose a particular flight. The importance of an attribute can be calculated byexamining the range of utilities (that is, the difference between the lowest and highestutilities) across all levels of the attribute. That range represents the maximum impactthat the attribute can contribute to a product.

Using the hypothetical utilities presented earlier, we can calculate the relativeimportance of each of the three attributes. The range for each attribute is given below:

· Duration: Range = 20 (42-22)· Comfort: Range = 3 (15-12)· Cost: Range = 56 (61-5)

These ranges tell us the relative importance of each attribute. Cost is the most importantfactor in product purchase as it has the highest range of utility values. Cost is followed inimportance by the duration of the flight. Based on the range and value of the utilities, wecan see that seat comfort is relatively unimportant to this consumer. Therefore,advertising which emphasizes seat comfort would be ineffective. This person will makehis or her purchase choice based mainly on cost and then on the duration of the flight.

Marketers can use the information from utility values to design products and/or serviceswhich come closest to satisfying important consumer segments. Conjoint analysis willidentify the relative contributions of each feature to the choice process. This technique,therefore, can be used to identify market opportunities by exploring the potential ofproduct feature combinations that are not currently available.

Choice Simulations

In addition to providing information on the importance of product features, conjointanalysis provides the opportunity to conduct computer choice simulations. Choicesimulations reveal consumer preference for specific products defined by the researcher.In this case, simulations will identify successful and unsuccessful flight packages beforethey are introduced to the market!

For example, let's say that the researcher defined three flights as follows:

The conjoint simulation will indicate the percentage of consumers that prefer each ofthe three flights. The simulation might show that consumers are willing to travel longerif they can pay less and are provided a meal. Simulations allow the researcher toestimate preference, sales and share for new flights before they come to market.

Simulations can be done interactively on a microcomputer to quickly and easily look atall possible options. The researcher may, for example, want to determine if a pricechange of Rs.50, Rs.100, or Rs.150 will influence consumer's choice. Also, conjoint willlet the researcher look at interactions among attributes. For example, consumers may bewilling to pay Rs.50 more for a flight on the condition that they are provided with a hotmeal rather than a snack.

Data Collection

Respondents are shown a set of products, prototypes, mock-ups or pictures. Eachexample is similar enough that consumers will see them as close substitutes, butdissimilar enough that respondents can clearly determine a preference. Each example iscomposed of a unique combination of product features. The data may consist ofindividual ratings, rank-orders, or preferences among alternative combinations. Thelatter is referred to as "choice based conjoint" or "discrete choice analysis".

In order to conduct a conjoint analysis, information must be collected from a sample ofconsumers. This data can be conveniently collected in locations such as shoppingcenters or by the Internet. In the previous example, data collection could take place at abooth located in an airport or in the office of a travel agent.

A sample size of 400 is generally sufficient to provide reliable data for consumerproducts or services. Data collection involves showing respondents a series of cards thatcontain a written description of the product or service. If a consumer product is beingtested then a picture of the product can be included along with a written description. Atypical card examining the business traveller might look like the following:

Readers might be worried at this point about the total number of cards that need to berated by a single respondent. Fortunately, we are able to use statistical manipulations tocut down on the number of cards. In a typical conjoint study, respondents only need torate between 10-20 cards.

This data would be input to the conjoint analysis. Utilities can then be calculated andsimulations can be performed to identify which products will be successful and whichshould be changed. Price simulations can also be conducted to determine sensitivity ofthe consumer to changes in prices.

A wide variety of companies and service organizations have successfully used conjointanalysis

A conjoint analysis was developed using a number of attributes such as saving on energybills, efficiency rating of equipment, safety record of energy source, and dependability ofenergy source. The conjoint analysis identified that cost savings and efficiency were themain reasons for converting appliances to gas. The third most important reason wascleanliness of energy source. This information was used in marketing campaigns inorder to have the greatest effect.

A natural gas utility used conjoint analysis to evaluate which advertising message wouldbe most effective in convincing consumers to switch from other energies to natural gas.Previous research failed to discover customer's specific priorities - it appeared that thetrade-offs that people made were quite subtle.

Advantages

· Able to use physical objects· Measures preferences at the individual level· Estimates psychological tradeoffs that consumers make when evaluating several

attributes together

Disadvantages

· Only a limited set of features can be used because the number of combinationsincreases very quickly as more features are added.

· Information gathering stage is complex.· Difficult to use for product positioning research because there is no procedure for

converting perceptions about actual features to perceptions about a reduced setof underlying features

· Respondents are unable to articulate attitudes toward new categories

Applications of conjoint analysis

Conjoint analysis has been used in marketing for a variety of purposes, including:

· Determining the relative importance of attributes in the consumer choiceprocess. A standard output from conjoint analysis consists of derived relativeimportance weights for all the attributes used to construct the stimuli used in theevaluation task. The relative importance weights indicate which attributes areimportant in influencing consumer choice.

· Estimating market share of brands that differ in attribute levels. The utilitiesderived from conjoint analysis can be used as input into a choice simulator todetermine the share of choices, and hence the market share, of different brands.

· Determining the composition of the most-preferred brand. The brand featurescan be varied in terms of attribute levels and the corresponding utilitiesdetermined. The brand features that yield the highest utility indicate thecomposition of the most-preferred brand.

· Segmenting the market based on similarity of preferences for attribute levels. Thepart worth functions derived for the attributes may be used as a basis forclustering respondents to arrive at homogenous preference segments.

Applications of conjoint analysis have been made in consumer goods, industrial goods,financial and other services. Moreover, these applications have spanned all areas ofmarketing. A recent survey of conjoint analysis reported applications in the areas of newproduct/concept identification, competitive analysis, pricing, market segmentation,advertising, and distribution.

SUMMARY

This chapter has given over view conjoint analysis in detail. Conjoint analysis, alsocalled multi-attribute compositional models. Today it is used in many of the socialsciences and applied sciences including marketing, product management, andoperations research.

KEY TERMS

· Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy· Residuals· Conjoint analysis

IMPORTANT QUESTIONS

1. What are the applications of conjoint analysis?

2. Explain the procedure of performing Conjoint Analysis with one practical example.

REFERENCE BOOKS

1. Robert Ferber, Marketing Research, New York: McGraw Hill, Inc. 1948

2. Dennis, Child, The Essentials of Factor Analysis, New York 1973

3. Cooley, William, W., and Lohnes, Paul R., Multivariate Data Analysis, New York:John Wiley and Sons. 1971.

- End of Chapter -

LESSON – 23

APPLICATION OF RESEARCH TOOLS

OBJECTIVES

· To identify the areas of management in which Research tools can be used· To understand the application of various research tools in the following domains

of management:

o Marketing Managemento Operations Managemento Human Resources Management

STRUCTURE

· Application of marketing research· Concept of market potential· Techniques of perceptual mapping· Limitation of Marketing Research· Methods of Forecasting· Statistical Methods

INTRODUCTION

Research Methodology is becoming a necessary tool for its application of all functionalareas of management such as Marketing, Human Resources and OperationsManagement. There is an increasing realisation of the importance of researchmethodology in various quarters. This is reflected in the increasing use of researchmethodology in various domains of management. Here, a brief description of typicalapplication of research methodology is given below:

APPLICATIONS OF MARKETING RESEARCH

Applications of marketing research can be divided into two broad areas:

· Strategic· Tactical

Among the strategic areas, marketing research applications would be demandforecasting, sales forecasting, segmentation studies, identification of target markets fora given product, and positioning strategies identification.

In the second area of tactical applications, we would have applications such as producttesting, pricing research, advertising research, promotional research, distribution andlogistics related research. In other words, it would include research related to all the 'P'sof marketing: how much to price the product, how to distribute it, whether to package itin one way or another, what time to offer a service, consumer satisfaction with respect tothe different elements of the marketing mix (product, price, promotion, distribution),and so on. In general, we would find more tactical applications than strategicapplications because these areas can be fine-tuned more easily, based on the marketingresearch findings.

Obviously, strategic changes are likely to be fewer than tactical changes. Therefore, theneed for information would be in proportion to the frequency of changes.

The following list is a snapshot of the kind of studies that have actually been done inIndia:

· A study of consumer buying habits for detergents-frequency, pack size, effect ofpromotions, brand loyalty and so forth.

· To find out the potential demand for ready-to-eat chapattis in Mumbai city.· To determine which of the three proposed ingredients – tulsi, coconut oil, or

neem – that the consumer would like to have in a toilet soap· To find out what factors would affect the sales of Flue Gas Desulphurization

equipment {industrial pollution control equipment)· To find out the effectiveness of the advertising campaign for a car brand· To determine brand awareness and brand loyalty for a branded PC (Personal

Computer)· To determine appropriate product mix, price level, and target market for a new

restaurant· To find the customer satisfaction level among consumers of an Internet service

provider· To determine factors which influenced consumers in choosing a brand of cellular

phone handset· To find out the TV viewing preferences of the target audience in specific time

slots in early and late evenings

As the list shows, marketing research tackles a wide variety of subjects. The list is onlyindicative, and the applications of marketing research in reality can be useful for almost

any major decision related to marketing. The next sections discuss some typicalapplication areas.

Concept Research

During a new product launch, there would be several stages-for example, conceptdevelopment, concept testing, prototype development and testing, test marketing in adesignated city or region, estimation of total market size based on the test marketing,and then a national rollout or withdrawal of the product based on the results.

The first stage is the development of a concept and its testing. The concept for a newproduct may come from several sources-the idea may be from a brain storming sessionconsisting of company employees, a focus group conducted among consumers, or thebrainwave of a top executive. Whatever may be its source, it is generally researchedfurther through what is termed as concept testing, before it goes into prototype orproduct development stages.

A concept test takes the form of developing a description of the product, its benefits,how to use it, and so on, in about a paragraph, and then asking potential consumers torate how much they like the concept, how much they would be willing to pay for theproduct if introduced, and similar questions. As an example, the concept statement for afabric softener may read as follows.

This fabric softener cum whitener is to be added to the wash cycle in a machine or to thebucket of detergent in which clothes are soaked. Only a few drops of this liquid will beneeded per wash to whiten white clothes and also soften them by eliminating staticcharge. It will be particularly useful for woolens, undergarments and baby’s or children’sclothes. It will have a fresh fragrance, and will be sold in handy 200 ml, bottles to lastabout a month. It can also replace all existing blues with the added benefit of a softener.

This statement can be used to survey existing customers of 'blues' and whiteners, and wecould ask customers for their reactions on pack size, pricing, colour of the liquid, ease ofuse, and whether or not they would buy such a product. More complex concept tests canbe done using Conjoint Analysis where specific levels of price or product/servicefeatures to be offered are pre-determined and reactions of consumers are in the form ofratings given to each product concept combining various features. This is then used tomake predictions about which product concepts would provide the highest utility to theconsumer, and to estimate market shares of each concept. The technique of ConjointAnalysis is discussed with an example in Part II of the book.

Product Research

Apart from product concepts, research helps to identify which alternative packaging ismost preferred, or what drives a consumer to buy a brand or product category itself, andspecifics of satisfaction or dissatisfaction with elements of a product. These days, serviceelements are as important as product features, because competition is bringing mostproducts on par with each other.

An example of product research would be to find out the reactions of consumers tomanual cameras versus automatic cameras. In addition to specific likes or dislikes foreach product category, brand preferences within the category could form a part of theresearch. The objectives may be to find out what type of camera to launch and howstrong the brand salience for the sponsor's brand is.

Another example of product research could be to find out from existing users ofphotocopiers (both commercial and corporate), whether after-sales service issatisfactory, whether spare parts are reasonably priced and easily available, and anyother service improvement ideas - for instance, service contracts, leasing options or buy-backs and trade-ins.

The scope of product research is immense, and includes products or brands at variousstages of the product life cycle-introduction, growth, maturity, and decline. Oneparticularly interesting category of research is into the subject of brand positioning. Themost commonly used technique for brand positioning studies (though not the only one)is called Multidimensional Scaling. This is covered in more detail with an example andcase studies in Part II as a separate chapter.

Pricing Research

Pricing is an important part of the marketing plan. In the late nineties in India, someinteresting changes have been tried by marketers of various goods and services. Newervarieties of discounting practices including buy-backs, exchange -offers, and straightdiscounts have been offered by many consumer durable manufacturers-notably AKAIand AIWA brands of TVs. Most FMCG (fast moving consumer goods)manufacturers/marketers of toothpaste, toothbrush, toilet soap, talcum powder haveoffered a variety of price-offs or premium-based offers which affect the effectiveconsumer price of a product.

Pricing research can delve into questions such as appropriate pricing levels from thecustomers' point of view, or the dealer's point of view. It could try to find out how thecurrent price of a product is perceived, whether it is a barrier for purchase, how a brandis perceived with respect to its price and relative to other brands' prices (pricepositioning). Here, it is worth remembering that price has a functional role as well as apsychological role. For instance, high price may be an indicator of high quality or highesteem value for certain customer segments. Therefore, questions regarding price mayneed careful framing and careful interpretation during the analysis.

Associating price with value is a delicate task, which may require indirect methods ofresearch at times. A bland question such as - "Do you think the price of Brand A ofrefrigerators is appropriate?" may or may not elicit true responses from customers. It isalso not easy for a customer to articulate the price he would be willing to pay forconvenience of use, easy product availability, good after-sales service, and otherelements of the marketing mix. It may require experience of several pricing-relatedstudies before one begins to appreciate the nuances of consumer behaviour related toprice as a functional and psychological measure of the value of a product offering.

An interesting area of research into pricing has been determining price elasticity atvarious price points for a given brand through experiments or simulations. Priceframing, or what the consumer compares (frames) price against, is another area ofresearch. For example, one consumer may compare the price of a car against anexpensive two-wheeler (his frame of reference), whereas another may compare it withan investment in the stock market or real estate. Another example might be the interestearned from a fixed deposit, which serves as a benchmark for one person before hedecides to invest in a mutual fund, whereas for another, the investment may be asubstitute for buying gold, which earns no interest. In many cases, therefore, it is theframe of reference used by the customer which determines 'value' for him of a givenproduct. There are tangible as well as intangible (and sometimes not discernible)aspects to a consumer's evaluation of price. Some of the case studies at the end of Part Iinclude pricing or price-related issues as part of the case.

Distribution Research

Traditionally, most marketing research focuses on consumers or buyers. Sometimes thisextends to potential buyers or those who were buyers but have switched to other brands.But right now, there is a renewed interest in the entire area of logistics, supply chain,and customer service at dealer locations. There is also increasing standardisation fromthe point of view of brand building, in displays at the retail level, promotions done at thedistribution points. Distribution research focuses on various issues related to thedistribution of products including service levels provided by current channels, frequencyof sales persons’ visits to distribution points, routing/transport related issues fordeliveries to and from distribution points throughout the channel, testing of newchannels, channel displays, linkages between displays and sales performance, and so on.As an example, a biscuit manufacturer wanted to know how it could increase sales of aparticular brand of biscuits in cinema theatres. Should it use existing concessionairesselling assorted goods in theatres, or work out some exclusive arrangements? Similarly,a soft drink manufacturer may want to know where to set up vending machines.Potential sites could include roadside stalls, shopping malls, educational institutions,and cinema theatres. Research would help identify factors that would make a particularlocation a success.

In many service businesses where a customer has to visit the location, it becomes veryimportant to research the location itself. For example, a big hotel or a specialtyrestaurant may want to know where to locate themselves for better visibility andoccupancy rates. Distribution research helps answer many of these questions andthereby make better marketing decisions.

Advertising Research

The two major categories of research in advertising are:

1. Copy

2. Media

Copy Testing

This is a broad term that includes research into all aspects of advertising-brandawareness, brand recall, copy recall (at various time periods such as day after recall,week after recall), recall of different parts of the advertisement such as the headline forprint ads, slogan or jingle for TV ads, the star in an endorsement and so on. Otherapplications include testing alternative ad copies (copy is the name given to text orwords used in the advertisement, and the person in the advertising agency responsiblefor writing the words is known as the copy writer) :or a single ad, alternative layouts (alayout is the way all the elements of, the advertisement are laid out in a printadvertisement) with the same copy, testing of concepts or storyboards (a storyboard is ascene-by-scene drawing of a TV commercial which is like a rough version before the adis actually shot on film) of TV commercials to test for positive/negative reactions, andmany others. Some of these applications appear in our discussion of Analysis ofVariance (ANOVA) in Part II and some case studies elsewhere in the book.

A particular class of advertising research is known as Tracking Studies. When anadvertising campaign is running, periodic sample surveys known as tracking studies canbe conducted to evaluate the effect of the campaign over a long period of time such assix months or one year, or even longer. This may allow marketers to alter the advertisingtheme, content, media selection or frequency of airing / releasing advertisements andevaluate the effects. As opposed to a snapshot provided by a one-time survey, trackingstudies may provide a continuous or near-continuous monitoring mechanism. But here,one should be careful in assessing the impact of the advertising on sales, because otherfactors could change along with time. For example, the marketing programmes of thesponsor and the competitors could vary over time. The impact on sales could be due tothe combined effect of several factors.

Media Research

The major activity under this category is research into viewership of specific televisionprogrammes on various TV channels. There are specialised agencies like A.C. Nielsenworldwide which offer viewership data on a syndicated basis (i.e., to anyone who wantsto buy the data). In India, both ORG-MARG and IMRB offer this service. They providepeople meter data with brand names of TAM and INTAM which is used by advertisingagencies when they draw up media plans for their clients. Research could also focus onprint media and their readership. Here again, readership surveys such as the NationalReadership Survey (NRS) and the Indian Readership Survey (IRS) provide syndicatedreadership data. These surveys are now conducted almost on a continuous basis in Indiaand are helpful to find out circulation and readership figures of major print media. ABC(Audit Bureau of Circulations) is an autonomous body which provides audited figures onthe paid circulation (number of copies printed and sold) of each newspaper andmagazine, which is a member of ABC.

Media research can also focus on demographic details of people reached by eachmedium, and also attempt to correlate consumption habits of these groups with theirmedia preferences. Advertising research is used at all stages of advertising, from

conception to release of ads and thereafter to measure advertising effectiveness basedon various parameters. It is a very important area of research for brands that rely a loton advertising. The top rated programmes in India are usually cricket matches and filmbased programmes.

Sales Analysis by Product

Sales analysis by product will enable a company to identify its strong or weak products.It is advisable to undertake an analysis on the basis of a detailed break-up of -productssuch as product variation by size, colour, etc. This is because if an analysis is based on abroad break-up, it may not reveal important variations.

When a company finds that a particular product is doing poorly, two Options are opento it. One is, it may concentrate on that product to ensure improved sales. Oralternatively, it may gradually withdraw the product and eventually drop it altogether.However, it is advisable to decide on the latter course on the basis of additionalinformation such as trends in the market share, contribution margin, and effect of salesvolume on product profitability, etc. In case the product in question hascomplementarity with other items sold by the company, the decision to abandon theproduct must be made with care and caution.

Combining sales analysis by product with that by territory will further help in providinginformation on which products are doing better in which areas.

Sales Analysis by Customers

Another way to analyse sales data is by customers. Such an analysis would normallyindicate that a relatively small number of customers accounts for a large proportion ofsales. To put it differently: a large percentage of customers accounts for a relativelysmall percentage of aggregate sales. One may compare the data with the proportion oftime spent on the customers, i.e. the number of sales calls. An analysis of this type willenable the company to devote relatively more time to those customers who collectivelyaccount for proportionately larger sales.

Sales analysis by customer can also be combined with analysis both by area and product.Such an analysis will prove to be more revealing. For example, it may indicate that insome areas sales are not increasing with a particular type of customer though they havegrown fast in other areas. Information of this type will be extremely useful to thecompany as it identifies the weak spots where greater effort is called for.

Sales Analysis by Size of Order

Sales analysis by size of order may show that a large volume of sales is accompanied bylow profit and vice versa. In case cost accounting data are available by size of order, thiswould help in identifying sales where the costs are relatively high and the company isincurring a loss. Sales analysis by size of order can also be combined with that byproducts, areas and types of customers. Such a perceptive analysis would reveal useful

information to the company and enable it to make a more rational and effective effort inmaximizing its return from sales.

THE CONCEPT OF MARKET POTENTIAL

Market potential has been defined as "the maximum demand response possible for agiven group of customers within a well-defined geographic area for a given product orservice over a specified period of time under well-defined competitive andenvironmental conditions".

We will elaborate this comprehensive definition. First, market potential is the maximumdemand response under certain assumptions. It denotes a meaningful boundarycondition on ultimate demand.

Another condition on which the concept of market potential depends is a set of relevantconsumers of the product or service. It is not merely the present consumer who is to beincluded but also the potential consumer as maximum possible demand is to beachieved. Market potential will vary depending on which particular group of consumersis of interest.

Further, the geographic area for which market potential is to be determined should bewell-defined. It should be divided into mutually exclusive subsets of consumers so thatthe management can assign a sales force and supervise and control the activities indifferent territories without much difficulty.

Another relevant aspect in understanding the concept of market potential is to clearlyknow the product or service for which market potential is to be estimated. Especially inthose cases where the product in question can be substituted by another, it is desirableto have market potential for the product class rather than that particular product. Forexample, tea is subjected to a high degree of cross-elasticity of demand with coffee.

It is necessary to specify the time period for which market potential is to be estimated.The time period should be so chosen that it coincides with planning periods in a firm.Both short and long-time periods can be used depending on the requirements of thefirm.

Finally, a clear understanding of environmental and competitive conditions relevant incase of a particular product or service is necessary if market potential is to be useful.What is likely to be the external environment? What is likely to be the nature and extentof competition? These are relevant questions in the context of any estimate of marketpotential since these are the factors over which the firm has no control.

It may be emphasised that market potential is not the same thing as sales potential andsales forecast. It is only when "a market is saturated can the industry sales forecast beconsidered equivalent to market potential". Such a condition is possible in case of wellestablished and mature products. Generally, the industry sales forecast will be less thanthe market potential. Likewise, a company's sales forecast will be less than its sales

potential. The former is a point estimate of the future sales, while the latter represents aboundary condition which the sales might reach in an ideal situation. "In the lattersense, sales potential is to a firm what market potential is to an industry or productclass: both represent maximum demand response and are boundary conditions".

Brand Positioning

Brand positioning is a relatively new concept in marketing. The concept owes its originto the idea that each brand occupies a particular space in the consumer's mind,signifying his perception of the brand in question in relation to other brands. Whileproduct or brand positioning has been defined by various authors in different ways, theunderlying meaning conveyed through these definitions seems to be the same. Insteadof giving several definitions, we may give one here. According to Green and Tull,

"Brand positioning and market segmentation appear to be the hallmarks of today'smarketing research. Brand (or service) positioning deals with measuring the perceptionsthat buyers hold about alternative offerings".

From this definition it is evident that the term 'position' reflects the essence of a brandas perceived by the target consumer in relation to other brands. In view of this themanagement's ability to position its product or brand appropriately in the market can bea major source of company's profits. This seems to be an important reason for theemergence of product or brand positioning as a major area in marketing research.

Components of Positioning

Positioning comprises four components. The first component is the product class or thestructure of the market in which a company's brand will compete. The secondcomponent is consumer segmentation. One cannot think of positioning a brand withoutconsidering the segment m which it is to be offered. Positioning and segmentation areinseparable. The third component is the consumers’ perception of the company's brandin relation to those of the competitors. Perceptual mapping is the device by which thecompany can know this. Finally, the fourth component positioning is the benefit offeredby the company's brand. A consumer can allot a position in his mind to a brand onlywhen it is beneficial to him. The benefits may be expressed as attributes or dimensionsin a chart where brands are fitted to indicate the consumer's perceptions.

As perceptual maps are used to indicate brand positioning, blank spaces in such mapsshow that a company can position its brand in one or more of such spaces.

TECHNIQUES FOR PERCEPTUAL MAPPING

There are a number of techniques for measuring product positioning. Some of thesewhich are important are:

· Factor analysis· Cluster analysis Multi-dimensional scaling.

We will not go into the detailed mechanism of these techniques. All the same, we willbriefly explain the techniques.

Image profile analysis

This technique is the oldest and most frequently used for measuring the consumer’sperceptions of competitive brands or services. Normally, a 5 or 7 point numerical scaleused. A number of functional and psychological attributes are selected. The respondentis asked to show his perception of each brand in respect of each attribute on the 5 or 7point scale.

It will be seen that the figures provides some insight as to which brands are competingwith each other and on what attribute(s). This technique has some limitations. First, ifthe number of brands is large, it may not be possible to plot all the brands in a singlefigure. Second, there is an implicit assumption in this technique that all attributes areequally important and independent of each other. This is usually not true. However, thislimitation can be overcome by using the technique of factor analysis.

Factor analysis

As regards factor analysis, it may be pointed out that its main object is to reduce a largenumber of variables into a small number of factors or dimensions. In Chapter 17, twoexamples have been given to illustrate the use of factor analysis. The discussion alsobrings out some major limitations of the method.

Cluster analysis

Cluster analysis is used to classify consumers or objects into a small number of mutuallyexclusive and exhaustive groups. With, the help of cluster analysis it is possible toseparate brands into clusters or groups so that the brand within a cluster is similar toother brands belonging to the same cluster and is very different from brands included inother clusters. This method has been discussed in Chapter

Multi-dimensional scaling

Multi-dimensional scaling too has been discussed in Chapter 17, pointing out howperceptual maps can be developed on the basis of responses from consumers. In thisconnection, two illustrations of perceptual maps were given. The first illustration relatedto select Business Schools based on hypothetical data On the basis of two criteria, viz.how prestigious and quantitative an MBA course is different Business Schools have beenshown in the map. It will be seen that the MBA course of Business School 'C is extremelydifferent from that offered by Business School Q Points which are close to each otherindicate similarity of the MBA courses in the students perception. The secondillustration related to four brands of washing soaps based on a survey data fromCalcutta. This is a non-attribute based example where a paired comparison for fourhigh- and-medium-priced detergents Surf, Sunlight, Gnat and Key was undertaken. Asmentioned there, Sunlight and Surf are closest and Surf and Key are farthest. In other

words the first two brands are most similar and the remaining two are most dissimilar.How the points in the figures for the four brands have been arrived at has beenexplained at length in that chapter and so is not repeated here.

Subroto Sengupta has discussed at length product positioning in his book. Whileexplaining different techniques of product positioning, he has shown how the concept ofpositioning can be used to improve the image of the concerned product or brand. He hasgiven a number of examples covering a wide variety of products such as coffee, softdrinks, washing soaps, toilet soaps, shampoos and magazines As Sengupta points outthe perceptual maps of product class also indicate holes or vacant positions in themarket. These open spaces can be helpful to the management in suggesting new productopportunities as also possibilities for repositioning of old products. While it is true thatthe management does get the clues on preferred attributes of the product in question, itis unable to know all the relevant features of the new product such as its form, packageand price. This problem can be overcome through the application of the conjointanalysis. In addition, Sengupta has discussed some research studies in respect ofadvertising positioning.

We now give a detailed version of a study indicating how a brand which was putting up apoor performance in the market was repositioned. As a result, it improved its image andcontributed to increased market share and profits.

When to do Marketing Research?

Marketing research can be done when:

o There is an information gap which can be filled by doing research.o The cost of filling the gap through marketing research is less than the cost of

taking a wrong decision without doing the research.o The time taken for the research does not delay decision-making beyond

reasonable limits.o A delay can have many undesirable effects, like competitors becoming aware of

strategies or tactics being. Contemplated, consumer opinion changing betweenthe beginning and end of the study, and so forth.

LIMITATIONS OF MARKETING RESEARCH

It must be kept in mind that marketing research, though very useful most of the time, isnot the only input for decision-making. For example, many small businesses workwithout doing marketing research, and some of them are quite successful. It is obviouslysome other model of informal perceptions about consumer behaviour, needs, andexpectations that is at work in such cases. Many businessmen and managers base theirwork on judgment, intuition, and perceptions rather than numerical data.

There is a famous example in India, where a company commissioned a marketingresearch company to find out if there was adequate demand for launching a newcamera. This was in pre-liberalised India, of the early 1980s. The finding of the research

study was that there was no demand, and that the camera would not succeed, iflaunched. The company went ahead and launched it anyway, and it was a huge success.The camera was Hot Shot. It was able to tap into the need of consumers at that time foran easy-to-use camera at an affordable price.

Thus marketing research is not always the best or only source of information to be usedfor making decisions. It works best when combined with judgment, intuition,experience, and passion. For instance, even if marketing research were to show therewas demand for a certain type of product, it still depends on the design andimplementation of the appropriate marketing plans to make it succeed. Further,competitors could take actions which were not foreseen when marketing research wasundertaken. This also leads us to conclude that the time taken for research should be theminimum possible, if we expect the conditions to be dynamic, or fast changing.

Differences in Methodology

The reader may be familiar with research studies or opinion polls conducted by differentagencies showing different results. One of the reasons why results differ is because themethodology followed by each agency is usually different. The sampling method used,the sample size itself, the representativeness of the population, the quality of field staffwho conduct interviews, and conceptual skills in design and interpretation all differfrom agency to agency. Minor differences are to be expected in sample surveys done bydifferent people, hut major differences should be examined for the cause, which willusually lead us to the different methodologies adopted by them. Based on the credibilityof the agency doing the research and the appropriateness of the methodology followed,the user decides which result to rely upon. A judgment of which methodology is moreappropriate for the research on hand comes from experience of doing a variety ofresearch.

To summarise, it is important to understand the limitations of marketing research, andto use it in such a way that we minimise its limitations.

Complementary Inputs for Decision-Making

Along with marketing research, marketing managers may need to look into otherinformation while making a decision. For example, our corporate policy may dictate thata premium image must be maintained in all activities of our company. On the otherhand, marketing research may tell us that consumers want a value-for-money product.This creates a dilemma for the basic corporate policy, which has to be balanced withconsumer perception as measured by marketing research.

Other inputs for decision-making could be growth strategies for the brand or product,competitors' strategies, and regulatory moves by the government and others. Some ofthese are available internally-for example, corporate policy and growth plans may bedocumented internally. Some other inputs may come from a marketing intelligence cellif the company has one. In any case, marketing decisions would be based on many ofthese complementary inputs, and not on the marketing research results alone.

Secondary and Primary Research

One of the most basic differentiations is between secondary and primary research.Secondary research is any information we may use, but which has not been specificallycollected for the current marketing research. This includes published sources of data,periodicals, newspaper reports, and nowadays, the Internet. It is sometimes possible todo a lot of good secondary research and get useful information. But marketing researchtypically requires a lot of current data which is not available from secondary sources.For example, the customer satisfaction level for a product or brand may not be reportedanywhere. The effectiveness of a particular advertisement may be evident from the saleswhich follow. But why people liked the advertisement may not be obvious, and can onlybe ascertained through interviews with consumers. Also, the methodology for thesecondary data already collected may be unknown, and therefore we may be unable tojudge the reliability and validity of the data.

Primary research is what we will be dealing with throughout this book. It can be definedas research which involves collecting information specifically for the study on hand,from the actual sources such as consumers, dealers or other entities involved in theresearch. The obvious advantages of primary research are that it is timely, focused, andinvolves no unnecessary data collection, which could be a wasted effort. Thedisadvantage could be that it is expensive to collect primary data. But when aninformation gap exists, the cost could be more than compensated by better decisions,which are taken with the collected data.

Thus Research has become a significant element of successful Marketing System. Thefollowing section speaks about application of Research in Operation/ProductionManagement domains.

Applications of Research Methodology in Operations Management

Methods of Estimating Current Demand

There are two types of estimates of current demand which may be helpful to a company.These are: total market potential and territory potential. "Total market potential is themaximum amount of sales that might be available to all the firms in an industry duringa given period under a given level- of industry marketing effort and given environmentalconditions".

Symbolically, total market potential is:

Q=n x q x p

where

Q = total market potential

n = number of buyers in the specific product/market under the given assumptions

q = quantity purchased by an average buyer

p = price of an average unit

Of the three components n, q, and p in the above formula, the most difficult componentto estimate is q. One can start with a broad concept of q, gradually reducing it. Forexample, if we are thinking of readymade shirts for home consumption, we may firsttake the total male population eliminating that in rural areas. From the total male urbanpopulation, we may eliminate the age groups which are not likely to buy readymadeshirts. Thus, the number of boys below 20 may be eliminated. Further eliminations onaccount of low income may be made. In this way we can arrive at the 'prospect pool' ofthose who are likely to buy shirts.

The concept of market potential is helpful to the firm as it provides a benchmark againstwhich actual performance can be measured. In addition, it can be used as a basis forallocation decisions regarding marketing effort.

The estimate of total market potential is helpful to the company when it is in a dilemmawhether to introduce a new product or drop an existing one. Such an estimate willindicate whether the prospective market is large enough to justify the company'sentering it.

Since it is impossible for a company to have the global market exclusively to itself, it hasto select those territories where it can sell its products well. This means that companiesshould know the territorial potentials so that they can select markets most suited tothem, channelise their marketing effort optimally among these markets and alsoevaluate their sale performance in such markets.

There are two methods for estimating territorial potentials: (i) market-buildup method,and (ii) index-of-buying-power method. In the first method, several steps are involved.First, identify all the potential buyers for the product in each market. Second, estimatepotential purchases by each potential buyer. Third, sum up the individual figures in step(ii) above. However, in reality the estimation is not that simple as it is difficult toidentify all potential buyers. When the product in question is an industrial product,directories of manufacturers of a particular product or group of products are used.Alternatively, the Standard Industrial Classification of Manufacturers of a particularproduct or group of products is used.

The second method involves the use of a straight forward index. Suppose a textilemanufacturing company is interested in knowing the territorial potential for its cloth ina certain territory. Symbolically,

Bi = 0.5Yi + 0.2ri + 0.3Pi

where

Bi = percentage of total national buying power in territory i

Yi = percentage of national disposable personal income originating in territory i

ri = percentage of national retail sales in territory i

Pi = percentage of national population living in territory i

It may be noted that such estimates indicate potential for the industry as a whole ratherthan for individual company. In order to arrive at a company potential, the concernedcompany has to make certain adjustments in the above estimate on the basis of one ormore other factors that have not been covered in the estimation of territorial potential.These factors could be the company's brand share, lumber of salespersons, number andtype of competitors, etc.

Forecasting Process

After having described the methods of estimating the current demand, we now turn toforecasting. There are five steps involved in the forecasting process. These arementioned below.

First, one has to decide the objective of the forecast. The marketing researcher shouldknow as to what will be the use of the forecast he is going to make.

Second, the time period for which the forecast is to be made should be selected. Is theforecast short-term, medium-term or long-term? Why should a particular period offorecast be selected?

Third, the method or technique of forecasting should be selected. One should be clearas to why a particular technique from amongst several techniques should be used.

Fourth, the necessary data should be collected. The need for specific data will dependon the forecasting technique to be used.

Finally, the forecast is to be made. This will involve the use of computationalprocedures.

In order to ensure that the forecast is really useful to the company, there should be goodunderstanding between management and research. The management should clearlyspell out the purpose of the forecast and how it is going to help the company. It shouldalso ensure that the researcher has a proper understanding of the operations of thecompany, its environment, past performance in terms of key indicators and theirrelevance to the future trend. If the researcher is well-informed with respect to theseaspects, then he is likely to make a more realistic and more useful forecast for themanagement.

Methods of Forecasting

The methods of forecasting can be divided into two broad categories, viz. subjective orqualitative methods and objective or quantitative methods. These can be further dividedinto several methods. Each of these methods is discussed below.

I. Subjective / Qualitative Methods

There are four subjective methods - field sales force, jury of executives, users'expectations and delphi. These are discussed here briefly.

a. Field sales force

Some companies ask their salesmen to indicate the most likely sales for a specifiedperiod in the future. Usually the salesman is asked to indicate anticipated sales for eachaccount in his territory. These forecasts are checked by district managers who forwardthem to the company's head office. Different territory-forecasts are then combined intoa composite forecast at the head office. This method is more suitable when a short-termforecast is to be made as there would be no major changes in this short period affectingthe forecast. Another advantage of this method is that it involves the entire sales forcewhich realises its responsibility to achieve the target it has set for itself. A majorlimitation of this method is that sales force would not take an overall or broadperspective and hence may overlook some vital factors influencing the sales. Anotherlimitation is that salesmen may give somewhat low figures in their forecasts thinkingthat it may be easier for them to achieve those targets. However, this can be offset to acertain extent by district managers who are supposed to check the forecasts.

b. Jury of executives

Some companies prefer to assign the task of sales forecasting to executives instead of asales force. Given this task each executive makes his forecast for the next period. Sinceeach has his own assessment of the environment and other relevant factors, one forecastis likely to be different from the other. In view of this it becomes necessary to have anaverage of these varying forecasts. Alternatively, steps should be taken to narrow downthe difference in the forecasts. Sometimes this is done by organising a discussionbetween the executives so that they can arrive at a common forecast. In case this is notpossible, the chief executive may have to decide which of these forecasts is acceptable asa representative one.

This method is simple. At the same time, it is based on a number of different viewpointsas opinions of different executives are sought. One major limitation of this method isthat the executives' opinions are likely to be influenced in one direction on the basis ofgeneral business conditions.

c. Users' expectations

Forecasts can be based on users' expectations or intentions to purchase goods andservices. It is difficult to use this method when the number of users is large. Anotherlimitation of this method is that though it indicates users' 'intentions' to buy, the actual

purchases may be far less at a subsequent period. It is most suitable when the number ofbuyers is small such as in case of industrial products.

d. The Delphi method

This method too is based on the experts' opinions. Here, each expert has access to thesame information that is available. A feedback system generally keeps them informed ofeach others' forecasts but no majority opinion is disclosed to them. However, the expertsare not brought together. This is to ensure that one or more vocal experts do notdominate other experts.

The experts are given an opportunity to compare their own previous forecasts with thoseof the others and revise them. After three or four rounds, the group of experts arrives ata final forecast.

The method may involve a large number of experts and this may delay the forecastconsiderably. Generally it involves a small number of participants ranging from 10 to40.

It will be seen that both the jury of executive opinion and the Delphi method are basedon a group of experts. They differ in that in the former, the group of experts meet,discuss the forecasts, and try To arrive at a commonly agreed forecast while in the latterthe group of experts never meet. As mentioned earlier, this is to ensure that no oneperson dominates the discussion thus influencing the forecast. In other words, theDelphi method retains the wisdom of a group and at the same time reduces the effect ofgroup pressure. An approach of this type is more appropriate when long-term forecastsare involved.

In the subjective methods, judgments are an important ingredient. Before attempting aforecast, the basic assumptions regarding environmental conditions as also competitivebehaviour must be provided people involved in forecasting. An important advantage ofsubjective methods is that they are easily understood. Another advantage is that the costinvolved in forecasting is quite low.

As against these advantages, subjective methods have certain limitations also. Onemajor limitation is the varying perceptions of people involved in forecasting. As a result,wide variance is found in forecasts. Subjective methods are suitable when forecasts areto be made for highly technical products which have a limited number of customers.Generally, such methods are used for industrial products. Also when cost of forecastingis to be kept to a minimum, subjective methods may be more suitable.

II. Objective / Quantitative or Statistical Methods

Based on statistical analysis, these methods enable the researcher to make forecasts on amore objective basis. It is difficult to make a wholly accurate forecast for there is alwaysan element of uncertainty regarding the future'. Even so, statistical methods are likely tobe more useful as they are more scientific and hence more objective.

a. Time Series

In time-series forecasting, the past sales data are extrapolated as a linear or a curvilineartrend. Even if such data are plotted on a graph, one can extrapolate for the desired timeperiod. Extrapolation can be made with the help of statistical techniques.

It may be noted that time-series forecasting is most suitable to stable situations wherethe future ids will largely be an extension of the past. Further, the past sales data shouldhave distinctive ids from the random error component for a time-series forecasting to besuitable.

Before using the time-series forecasting one has to decide how far back in the past onecan go. It may be desirable to use the more recent data as conditions might have beendifferent in the remote past. Another issue pertains to weighting of time-series data. Inother words, should equal weight be given to each time period or should greaterweightage be given to more recent data? Finally, should data be decomposed intodifferent components, viz. trend, cycle, season and error? We now discuss methods, viz.moving averages, exponential smoothing and decomposition of time series.

b. Moving average

This method uses the last 'n' data points to compute a series of average in such a waythat each time latest figure is used and the earliest one dropped. For example, when wehave to calculate a five monthly moving average, we first calculate the average ofJanuary, February, March, April and May by adding the figures of these months, anddividing the sum by five. This will give one figure. In the next calculation, the figure forJune will be included and that for January dropped thus giving a new average. Thus aseries of averages is computed. The method is called as 'moving' average as it uses wdata point each time and drops the earliest one.

In a short-term forecast, the random fluctuations in the data are of major concern. Onemethod of minimizing the influence of random error is to use an average of several pastdata points. This is achieved by the moving average method. It may be noted that in a12-month moving average, the effect of seasonality is removed from the forecast as datapoints for every season are included before computing the moving average.

c. Exponential smoothing

A method which has been receiving increasing attention in recent years is known asexponential smoothing. It is a type of moving average that 'smoothens' the time-series.When a large number of forecasts are to be made for a number of items, exponentialsmoothing is particularly suitable as it combines the advantages of simplicity ofcomputation and flexibility.

d. Time-series decomposition

This method consists of measuring the four components of a time-series (i) trend, (ii)cycle, (iii) season, and (iv) erratic movement.

(i) The trend component indicates long-term effects on sales that are caused bysuch factors as income, population, industrialisation and technology. The timeperiod a trend function varies considerably from product to product However, itis usually taken as any period in excess of the time period required for a businesscycle (which averages at 4-5 years).

(ii) The cyclical component indicates some sort of a periodicity in the generaleconomic activity. When data are plotted, they yield a curve with peaks andtroughs, indicating increases and falls in the trend series with a certainperiodicity. A careful study of the impact of a business cycle must be made on thesale of each product. Cyclical forecasts are likely to be more accurate for the long-term than for the short term.

(iii) The seasonal component reflects changes in sales levels due to factors such asweather, festivals, holidays, etc. There is a consistent pattern of sales for periodwithin a year.

(iv) Finally, the erratic movements in data arise on account of events such asstrikes, lockouts, price wars, etc. The decomposition of time-series enablesidentification of the error component from the trend, cycle and season which aresystematic components.

Casual or Explanatory Methods

Causal or explanatory methods are regarded as the most sophisticated methods offorecasting sales. These methods yield realistic forecasts provided relevant data areavailable on the- major variables influencing changes in sales. There are three distinctadvantages of causal methods. First, turning points in sales can be predicted moreaccurately by these methods than by time-series methods. Second, the use of thesemethods reduces the magnitude of the random component far more than it may bepossible with the time-series methods. Third, the use of such methods provides greaterinsight to causal relationships. This facilitates the management in marketing decisionmaking. Isolated sales recasts on the basis of time-series methods would not be helpfulin this regard.

Causal methods can be either (i) leading indicators or (ii) regression models. These arebriefly discussed here.

(i) Leading indicators

Sometimes one finds that changes in sales of a particular product or service arepreceded by changes one or more leading indicators. In such cases, it is necessary toidentify leading indicators and to closely observe changes in them. One example of aleading indicator is the demand for various household appliances which follows the

construction of new houses. Likewise, the demand for many durables is preceded by anincrease in disposable income. Yet another example is of number of births. The demandfor baby food and other goods needed by infants can be ascertained by the number ofbirths in a territory. It may be possible to include leading indicators in regressionmodels.

(ii) Regression models

Linear regression analysis is perhaps the most frequently used and the most powerfulmethod among casual methods. As we have discussed regression analysis in detail in thepreceding chapters on Bivariate Analysis and Multivariate Analysis, we shall only dwellon a few relevant points.

First, regression models indicate linear relationships within the range of observationsand at the les when they were made. For example, if a regression analysis of sales isattempted on the basis of independent variables of population sizes of 15 million to 30million and per capita income of Rs 1000 to Rs.2500, the regression model shows therelationships that existed between these extremes in the two independent variables. Ifthe sales forecast is to be made on the basis of values of independent variables fallingoutside the above ranges, then the relationships expressed by the regression model maynot hold good. Second, sometimes there may be a lagged relationship between thedependent and independent variables. In such cases, the values of dependent variablesare to be related to those of independent variables for the preceding month or year asthe case may be. The search for factors with a lead-lag relationship to the sales of aparticular product is rather difficult. One should tryout several indicators beforeselecting the one which is most satisfactory. Third, it may happen that the data requiredto establish the ideal relationship, do not exist or are inaccessible or, if available, are notuseful. Therefore, the researcher has to be careful in using the data. He should be quitefamiliar with the varied sources and types of data that can be used in forecasting. Heshould also know about their strengths and limitations. Finally, regression modelreflects the association among variables. The causal interpretation is done by theresearcher on the basis of his understanding of such an association. As such, he shouldbe extremely careful in choosing the variables so that a real causative relationship can beestablished among the variables chosen.

Input-Output Analysis

Another method that is widely used for forecasting is the input-output analysis. Here,the researcher takes into consideration a large number of factors, which affect theoutputs he is trying to forecast. For this purpose, an input-output table is prepared,where the inputs are shown horizontally as the column headings and the outputsvertically as the stubs. It may be mentioned that by themselves input-output flows are oflittle direct use to the researcher. It is the application of an assumption as to how theoutput of an industry is related to its use of various inputs that makes an input-outputanalysis a good method of forecasting. The assumption states that as the level of anindustry's output changes, the use of inputs will change proportionately, implying that

there is no substitution in production among the various inputs. This may or may nothold good.

The use of input-output analysis in sales forecasting is appropriate for products sold togovernmental, institutional and industrial markets as they have distinct patterns ofusage. It is seldom used for consumer products and services. It would be mostappropriate when the levels and kinds of inputs required achieving certain levels ofoutputs need to be known.

A major constraint in the use of this method is that it needs extensive data for a largenumber of items which may not be easily available. Large business organisations may bein a position to collect such data on a continuing basis so that they can use input-outputanalysis for forecasting. However, this is not possible m case of small industrialorganisations on account of excessive costs involved in the collection of comprehensivedata. It is for this reason that input, output analysis is less widely used than mostanalysts initially expected. A detailed discussion of input-output analysis is beyond thescope of this book.

Econometric Model

Econometrics is concerned with the use of statistical and mathematical techniques toverify hypotheses emerging in economic theory. "An econometric model incorporatesfunctional relationships between estimated techniques into an internally consistent andlogically self-contained framework". Econometrics use both exogenous and endogenousvariables. Exogenous variables are used as inputs into, but they themselves aredetermined outside the model. These variables include policy variables controlledevents. In contrast, endogenous variables are those which are determined within thesystem.

The use of econometric models is generally found at the macro level such as forecastingnational e and its components. Such models show how the economy or any of its specificsegments operates. As compared to an ordinary regression equation they bring out thecausalities involved more distinctly. This merit of econometric models enables them topredict turning points more accurately. However, their use at the micro-level forforecasting has so far been extremely limited.

Applications of research methodology in human resources management

Research methodology widely used in the domains of Human resources Management. Itis called as Human resources Metrics (HR Metrics).

To move to the center of the organization, HR must be able to talk in quantitative,objective terms. Organizations are managed by data. Unquestionably, at times,managers make decisions based on emotions as facts. Nevertheless, day-to-dayoperations are discussed, planned and evaluated in hard data terms.

Perhaps the most crucial advantage of a sound HR metrics programme is that it enablesHR to converse with senior management in the language of business. Operationaldecisions taken by HR are then based on cold, hard facts rather than gut feeling, thefigures being used to back up business cases and requests for resource. The HR functionis transformed from a bastion of 'soft' intangibles into something more 'scientific', betterable to punch its weight in the organisation. In addition, the value added by HRbecomes more visible. This will become increasingly important as more and morefunctions attempt to justify their status as strategic business partners rather than merelycost centres.

The five key practices of the Human Capital Index are as follows:

1. Recruiting excellence

2. Clear rewards and accountability,

3. Prudent use of resources,

4. Communications integrity

5. Collegial flexible workplace

· They require the capture of metrics for their very definition. Metrics helpquantify and demonstrate the value of HR

· Metrics can help guide workforce strategies and maximize return on HRinvestments

· Metrics provide measurement standards· Metrics help show what HR contributes to overall business results

SUMMARY

The above lesson has given brief introduction to various applications of various researchtechniques in management. It has identified the appropriate tools for applications ofvarious domains of Management.

KEY TERMS

· Marketing research· Brand positioning· Image profile analysis· Market Potential· Demand Measurement· Delphi Method· Time Series analysis· Moving average· HR Metrics

IMPORTANT QUESTIONS

1. What are all the various domains in which research tools can be used?2. Explain the application of Image profile analysis with example.3. Differentiate between Primary and secondary research.4. What are the limitations of marketing research?5. Describe the method for finding out the Market potential.6. Explain the Various methods to estimate the Demand.7. What do you mean by HR Metrics?8. Note down the five key practices of the Human Capital Index.

- End of Chapter -

LESSON - 24

REPORT PREPARATIONS

OBJECTIVES

· To learn the structure of Professional Research report· To understand the application of following diagrams

o Area Charto Line Grapho Bar charto Pie charto Radar diagramo Surface diagramo Scatter diagram

STRUCTURE

· Research report· Report format· Data presentation· Pareto chart

RESEARCH REPORT

The final step in the research process is the preparation and presentation of the researchreport. A research report can be defined as the presentation of the research findingsdirected to a specific audience to accomplish a specific purpose.

Importance of report

The research report is important for the following reasons:

1. The results of research can be effectively communicated to management.

2. The report is the only aspect of the study, which executives are exposed to and theirconsecutive evaluation of the project rests with the effectiveness of the written and oralpresentation.

3. The report presentations are typically the responsibility of the project worthiness. So,the communication effectiveness and usefulness of the information provided plays acrucial role in determining whether that project will be continued in future.

Steps in report preparation

Preparing a research report involves three steps

1. Understanding the research

2. Organizing the information

3. Writing with effectiveness

Guidelines

The general guidelines that should be followed for any report are as follows:

1. Consider the audience: The information resulting from research is ultimatelyimportant to the management, who will use the results to make decisions. Decisionmakers are interested in a clear, concise, accurate and interesting report, which directlyfocuses on their information needs with a minimum of technological jargons. Thus, thereport has to be understood by them; the report should not be too technical and not toomuch jargon should be used. This is a particular difficulty when reporting the results ofstatistical analysis where there is a high probability that few of the target audience havea grasp of statistical concepts. Hence, for example, there is a need to translate suchterms as standard deviation, significance level, confidence interval etc. into everydaylanguage.

2. Be concise, but precise: The real skill of the researcher is tested in fulfilling thisrequirement. The report must be concise and must focus on the crucial elements of theproject. It should not include the unimportant issues. Researcher should know howmuch emphasis has to be given to each area.

3. Be objective, yet effective: The research report must be an objective presentationof the research findings. The researcher violates the standard of objectivity if thefindings are presented in a distorted or slanted manner. The findings can be presentedin a manner, which is objective, yet effective. The writing style of the report should beinteresting, with the sentence structure short and to the point.

4. Understand the results and draw conclusions: The managers who read thereport are expecting to see interpretive conclusions in the report. The researcher shouldunderstand the results and be able to interpret it effectively to management. Simplyreiterating the facts will not do, implications has to be drawn using the "so what"questions on the results.

REPORT FORMAT

Every person has a different style of writing. There is not really one right style of writing,but the following outline is generally accepted as the basis format for most researchprojects.

1. Title Page2. Table of contents3. Executive summary4. Introduction5. Problem statement6. Research objective7. Background8. Methodology9. Sampling design10. Research design11. Data collection12. Data analysis13. Limitation14. Findings15. Conclusions16. Summary and conclusions17. Recommendations18. Appendices19. Bibliography

1. Title page

The title page should contain a title which conveys the essence of the study, the date, thename of the organization submitting the report, and the organization for whom there isprepared. If the research report is confidential, the name of those individuals to receivethe report should be specified on the title page.

2. Table of contents

As a rough guide, any report of several sections that totals more than 6/to 10 pagesshould have a table of contents. The table of contents lists the essence of topics coveredin the report, along with page references. Its purpose is to aid readers in finding aparticular section in the report. If there are many tables, charts, or other exhibits, theyshould also be listed after the table of contents in a separate table of illustrations.

3. Executive summary

An executive summary can serve two purposes. It may be a report in miniature coveringall the aspects in the body of the report, but in abbreviated form, or it may be a concisesummary of major findings and conclusions including recommendations.

Two pages are generally sufficient for executive summaries. Write this section after thereport is finished. It must exclude the new information but may require graphics topresent a particular conclusion.

Expect the summary to contain a high density of significant terms since it is repeatingthe highlights of report. A good summary should help the decision make and it isdesigned to be action oriented.

4. Introduction

The introduction prepares the reader for the report by describing the parts of theproject: the problem statement, research objectives and background material.

The introduction must clearly explain the nature of decision problem. It should reviewthe previous research done on the problem.

5. Problem statement

The problem statement contains the need for the research project. The problem isusually represented by a management questions. It is followed by a more detailed set ofobjectives.

6. Research objectives

The research objectives address the purpose of the project. These may be researchquestion(s) and associated investigative questions.

7. Background

The Background material may be of two types. It may be the preliminary results ofexploration from an experience survey, focus group, or another source. Alternatively itcould be secondary data from the literature review. Background material may be placedbefore the problem statement or after the research objectives. It contains informationpertinent to the management problem or the situation that led to the study.

8. Methodology

The purpose of the methodology section is to describe the nature of the research design,the sampling plain, data collection and analysis procedure. Enough details must beconveyed so that the reader can appreciate the nature the methodology used, yet thepresentation must not be boring overpowering. The use of technical jargon must beavoided.

9. Research design

The coverage of the design must be adapted to the purpose. The type of researchadapted and reason for adapting that particular type should d be explained.

10. Sampling design

The research explicitly defines the target population being studied and the samplingmethods used. It has to explain the sampling frame, sampling method adapted andsample size. Explanation of the sampling method, uniqueness of the chosen parametersor other relevant points that need explanation should be covered with brevity.Calculation of sample size can be placed either in this part or can be placed in anappendix.

11. Data collection

This part of report describes the specifics of gathering the data. Its content depends onthe selected design. The data collection instruments (questionnaire or interviewschedule) field instructions can be placed in the appendix.

12. Data analysis

This section summarizes the methods used to analyze the data. Describe data handling,preliminary analysis, statistical tests, computer programs and other technicalinformation. The rationale for the choice of analysis approaches should be clear. A briefcommentary on assumptions and appropriateness of use should be presented.

13. Limitations

Every project has weakness, which need to be communicated in a clear and concisemanner. In this process, the researcher should avoid belaboring minor study weakness.The purpose of this section is not to disparage the quality of the research project, butrather to enable the reader to judge the validity of the study results.

Generally the limitations will occur in sampling, no response inadequacies andmethodological weakness. It is the researcher's professional responsibility to clearlyinform the reader of these limitations.

14. Findings

The objective of this part is to explain the data rather than draw conclusions. Whenquantitative data can be presented, this should be done as simply as possible withcharts, graphics and tables.

The findings can be presented in a small table or chart on the same page. While thisarrangement adds to the bulk of the report, it is convenient for the reader.

15. Conclusions

It can be further divide into two parts as summary and recommendations.

16. Summary and conclusions

The summary is brief statement of the essential findings. The conclusion should clearlylink the research findings with the information needs, and based on this linkagerecommendation for action can be formulated. In some research works the conclusionswere presented in a tabular form for easy reading and reference. The research questions/objectives will be answered sharply in this part.

17. Recommendations

The researcher's recommendations may be weighed more heavily in favor of theresearch findings. There are few ideas about corrective actions. The recommendationsare given for managerial actions rather than research action. The researcher may offerseveral alternatives with justifications.

18. Appendices

The purpose of appendix is to provide a place for material, which is not absolutelyessential to the body of the report. The material is typically more specialized andcomplex than material presented in the main report, and it is designed to serve theneeds of the technically oriented reader. The appendix will frequently contain copies ofthe data collection forms, details of the sampling plan, estimates of statistical error,interviewer instructions and detailed statistical tables associated with the data analysisprocess. The reader who wishes to learn the technical aspects of the study and to look atstatistical breakdowns will want a complete appendix.

19. Bibliography

The use of secondary data requires a Bibliography. Proper citation, style and formats areunique to the purpose of the report. The instructor, program, institution, or client oftenspecifies style requirements. It will be given as footnote or endnote format. The authorname, title, publication, year, pager number are the important elements of bibliography.

DATA PRESENTATION

The research data can be presented in Tabular & Graphic form.

Tables

The tabular form consists of the numerical presentation of the data. Tables shouldcontain the following elements:

1. Table number, this permits easy location in the report

2. Title: the title should clearly indicate the contents of the table or figure.

3. Box head and sub head: the box head contains the captions or labels to the column ina table, while the sub head contains the labels for the rows.

4. Footnote: footnote explains the particular section or item in the table or figure.

Graphics

The graphical form involves the presentation of data in terms of visually interpretedsizes. Graphs should contain the following elements:

1. Graph or figure number

2. Title

3. Footnote

4. Sub heads in the axis

Bar chart

A bar chart depicts magnitudes of the data by the length of various bars which have beenlaid out with reference to a horizontal or vertical scale. The bar chart is easy to constructand can be readily interpreted.

Column chart

These graphs compare the sizes and amounts of categories usually for the same time.Mostly places the categories on X-axis and values on Y-axis.

Pie chart

The pie chart is a circle divided into sections such that the size of each sectioncorresponds to a portion of the total. It shows the relationship of parts to the whole.Wedges are row values of data. It is one form of area chart. This type is often used withbusiness data.

Line Graph

Line graphs are used chiefly for time series and frequency distribution. There are severalguidelines for designing the line graph.

· Put the independent variable in the horizontal axis· When showing more than one line, use different line types· Try not to put more than four lines on one chart· Use a solid line for the primary data.

I. Radar diagram

In this the radiating lines are categories; values are distances from the center. It can beapplied where multiple variables used.

II. Area (surface) diagram

An area chart is also used for a time series. Like line charts it compares changing valuesbut emphasis relative values of each series

III. Scatter diagram

This shows the values if there is relationship between variables follows a pattern; may beused with one variable at different times.

Purpose of a Histogram

A histogram is used to graphically summarize and display the distribution of a processdata set. The purpose of a histogram is to graphically summarize the distribution of auni-variate data set.

The histogram graphically shows the following:

1. center (i.e. the location) of the data;

2. spread (i.e. the scale) of the data;

3. skewness of the data;

4. presence of outliers; and

5. presence of multiple modes in the data.

These features provide strong indications of the proper distributional model for thedata. The probability plot or a goodness-of-fit test can be used to verify thedistributional model.

Sample Bar Chart Depiction

How to construct a Histogram

A histogram can be constructed by segmenting the range of the data into equal sizedbins (also called segments, groups or classes). For example, if your data ranges from 1.1to 1.8, you could have equal bins of 0.1 consisting of 1 to 1.1, 1.2 to 1.3, 1.3 to 1.4, and soon.

The vertical axis of the histogram is labeled Frequency (the number of counts for eachbin), and the horizontal axis of the histogram is labeled with the range of your responsevariable.

The most common form of the histogram is obtained by splitting the range of the datainto equal-sized bins (called classes). Then for each bin, the numbers of points from thedata set that fall into each bin are counted. That is,

- Vertical axis: Frequency (i.e., counts for each bin)

- Horizontal axis: Response variable

The classes can either be defined arbitrarily by the user or via some systematic rule. Anumber of theoretically derived rules have been proposed by Scott (Scott 1992).

The cumulative histogram is a variation of the histogram in which the vertical axis givesnot just the counts for a single bin, but rather gives the counts for that bin plus all binsfor smaller values of the response variable.

Both the histogram and cumulative histogram have an additional variant whereby thecounts are replaced by the normalized counts. The names for these variants are therelative histogram and the relative cumulative histogram.

There are two common ways to normalize the counts.

1. The normalized count is the count in a class divided by the total number ofobservations. In this case the relative counts are normalized to sum to one (or 100 if apercentage scale is used). This is the intuitive case where the height of the histogram barrepresents the proportion of the data in each class.

2. The normalized count is the count in the class divided by the number of observationstimes the class width. For this normalization, the area (or integral) under the histogramis equal to one. From a probabilistic point of view, this normalization results in a relativehistogram that is most akin to the probability density function and a relative cumulativehistogram that is most akin to the cumulative distribution function. If you want tooverlay a probability density or cumulative distribution function on top of the-histogram, use this normalization. Although this normalization is less intuitive (relativefrequencies greater than 1 are quite permissible), it is the appropriate normalization ifyou are using the histogram to model a probability density function.

What questions does Histogram Answer?

· What is the most common system response?· What distribution (center, variation and shape) does the data have?· Does the data look symmetric or is it skewed to the left or right?· Does the data contain outliers?

PARETO CHART

Purpose of a Pareto Chart

A Pareto Chart is used to graphically summarize and display the relative importance ofthe differences between groups of data. A bar graph used to arrange information in sucha way that priorities for process improvement can be established.

Sample Pareto Chart Depiction

Purposes

- To display the relative importance of data.

- To direct efforts to the biggest improvement opportunity by highlighting the vital fewin contrast to the useful many.

Pareto diagrams are named after Vilfredo Pareto, an Italian sociologist and economist,who invented this method of information presentation toward the end of the 19thcentury. The chart is similar to the histogram or bar chart, except that the bars arearranged in decreasing order from left to right along the abscissa. The fundamental ideabehind the use of Pareto diagrams for quality improvement is that the first few (aspresented on the diagram) contributing causes to a problem usually account for themajority of the result. Thus, targeting these "major causes" for elimination results in themost cost-effective improvement scheme.

How to Construct

· Determine the categories and the units for comparison of the data, such asfrequency, cost, or time.

· Total the raw data in each category, then determine the grand total by adding thetotals of each category. Re-order the categories from largest to smallest.

· Determine the cumulative percent of each category (i.e., the sum of each categoryplus all categories that precede it in the rank order, divided by the grand total andmultiplied by 100).

· Draw and label the left-hand vertical axis with the unit of comparison, such asfrequency, cost or time.

· Draw and label the horizontal axis with the categories. List from left to right inrank order.

· Draw and label the right-hand vertical axis from 0 to 100 percent. The 100percent should line up with the grand total on the left-hand vertical axis.

· Beginning with the largest category, draw in bars for each category representingthe total for that category.

· Draw a line graph beginning at the right-hand corner of the first bar to representthe cumulative percent for each category as measured on the right-hand axis.

· Analyze the chart. Usually the top 20% of the categories will comprise roughly80% of the cumulative total.

Guidelines for Effective applications of Pareto analysis:

· Create before and after comparisons of Pareto charts to show impact ofimprovement efforts.

· Construct Pareto charts using different measurement scales, frequency, cost ortime.

· Pareto charts are useful displays of data for presentations.· Use objective data to perform Pareto analysis rather than team members'

opinions.· If there is no clear distinction between the categories - if all bars are roughly the

same height or half of the categories are required to account for 60 percent of theeffect - consider organizing the data in a different manner and repeating Paretoanalysis.

What questions does the Pareto chart answer?

· What are the largest issues facing our team or business?· What 20% of sources are causing 80% of the problems (80/20 Rule)?· Where should we focus our efforts to achieve the greatest improvements?

Example of constructing the Pareto Chart

The following table shows the reasons for failure of patients in a Hospital:

Pareto chart for above details can be drawn as follows:

When to Use a Pareto Chart

Pareto charts are typically used to prioritize competing or conflicting "problems," so thatresources are allocated to the most significant areas. In general, though, they can beused to determine which of several classifications have the most "count" or costassociated with them. For instance, the number of people using the various ATM's vs.each of the indoor teller locations, or the profit generated from each of twenty productlines. The important limitations are that the data must be in terms of either counts orcosts. The data cannot be in terms that can't be added, such as percent yields or errorrates.

PICTOGRAPH

A pictograph is used to present statistics in a popular yet less statistical way to thosewho are not familiar with charts that contain numerical scales. This type of chartpresents data in the form of pictures drawn to represent comparative sizes, scales orareas.

Again as with every chart, the pictograph needs a title to describe what is beingpresented and how the data are classified as well as the time period and the source ofthe data.

Examples of these types of charts appear below:

A pictograph uses picture symbols to convey the meaning of statistical information.Pictographs should be used carefully because the graphs may, either accidentally ordeliberately, misrepresent the data. This is why a graph should be visually accurate. Ifnot drawn carefully, pictographs can be inaccurate

Stem Plots

In statistics, a Stemplot (or stem-and-leaf plot) is a graphical display of quantitative datathat is similar to a histogram and is useful in visualizing the shape of a distribution.They are generally associated with the Exploratory Data Analysis (EDA) ideas of JohnTukey and the course Statistics in Society (NDST242) of the Open University, althoughin fact Arthur Bowley did something very similar in the early 1900s.

Unlike histograms, Stemplots:

- retain the original data (at least the most important digits)

- put the data in order - thereby easing the move order-based inference and non-parametric statistics.

A basic Stemplot contains two columns separated by a vertical line. The left columncontains the stems and the right column contains the leaves. The ease with which

histograms can now be generated on computers has meant that Stemplots are less usedtoday than in the 1980's, when they first became widely used.

To construct a Stemplot, the observations must first be sorted in ascending order. Hereis the sorted set of data values that will be used in the example:

54 56 57 59 63 64 66 68 68 72 72 75 76 81 84 88 106

Next, it must be determined what the stems will represent and what the leaves willrepresent. Typically, the leaf contains the last digit of the number and the stem containsall of the other digits. In the case of very large or very small numbers, the data valuesmay be rounded to a particular place value (such as the hundreds place) that will beused for the leaves. The remaining digits to the left of the rounded place value are usedas the stems.

In this example, the leaf represents the ones place and the stem will represent the rest ofthe number (tens place and higher).

The Stemplot is drawn with two columns separated by a vertical line. The stems arelisted to the left of the vertical line. It is important that each stem is listed only once andthat no numbers are skipped, even if it means that some stems have no leaves. Theleaves are listed in increasing order in a row to the right of each stem.

Double Stem Plots (Stem-and-leaf Plot)

Splitting stems and the back-to-back stem plot are two distinct types of double stemplots, which are a variation of the basic stem plot.

Splitting Stems

On the data set, splitting each of the stems into two or five stems may better illustratethe shape of the distribution. When splitting stems, it is important to split all stems andto split the stems equally. When splitting each stem into two stems, one stem containsleaves from 0-4 and leaves from 5-9 are contained in the other stem. When splittingeach stem into five stems, one stem contains leaves 0-1, the next 2-3, the next 4-5, the

next 6-7, and the last leave 8-9. Here is an example of a split stem plot (using the samedata set from the example above) in which each stem is split into two:

SUMMARY

A research report can be defined as the presentation of the research findings directed toa specific audience to accomplish a specific purpose.

General guidelines followed to write the report are

1. Consider the audience,2. Be concise, but precise3. Be objective, yet effective &4. Understand the results and draw conclusions.

The main elements of report are title page, table of contents, executive summary,introduction, methodology, findings, conclusions, appendices, and bibliography.

Tables and graphs are used for the presentation of data. Different types of graphs areavailable like bar chart, pie chart, line chart, area diagram, radar diagram, scatterdiagram, etc. According to the nature of data and requirement the type of graph can beselected and used effectively.

KEY TERMS

· Executive summary· Sampling· Bibliography· Appendix· Interview schedule· Area chart· Line graph· Bar chart· Pie chart· Scatter diagram· Radar diagram· Surface diagram· Pareto Chart· Pictograph· Stem-graph

IMPORTANT QUESTIONS

1. What do you mean by research report?2. Why is the research report important?3. Explain the general guidelines exist for writing a report?4. What are the preparations required for writing the report?5. What components are typically included in a research report?6. What are the alternative means of displaying data graphically?7. Explain the application of Pareto Chart with example8. What are the applications of Pictograph?9. What are the procedures to draw Stem Graph or Stem Plot?

REFERENCE BOOKS

1. Ramanuj Majumdar, Marketing research, Wiley Estern Ltd., New Delhi, 1991.2. Harper W Boyd, Jr etal, Marketing Research, Richard D. Irevin Inc. USA 1990.3. Paul E. Green et al, Research for Marketing Decisions, Prentice Hall of India Pvt.

Ltd., New Delhi, 2004.

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