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Research Design : Research Design : Sampling & Sampling & Data Collection Data Collection MBA2216 BUSINESS RESEARCH PROJECT MBA2216 BUSINESS RESEARCH PROJECT by Stephen Ong Visiting Fellow, Birmingham City University, UK Visiting Professor, Shenzhen University
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Mba2216 week 09 10 sampling

Aug 29, 2014

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Stephen Ong

Sampling design, Sampling methods
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Page 1: Mba2216 week 09 10 sampling

Research Design :Research Design :Sampling &Sampling &

Data CollectionData Collection

MBA2216 BUSINESS RESEARCH PROJECTMBA2216 BUSINESS RESEARCH PROJECT

byStephen Ong

Visiting Fellow, Birmingham City University, UKVisiting Professor, Shenzhen University

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6-2

Design in the Research ProcessDesign in the Research Process

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14-3

Sampling Design Sampling Design within the Research Processwithin the Research Process

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Sampling DesignSampling Design

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LEARNING OUTCOMESLEARNING OUTCOMES

1. Explain reasons for taking a sample rather than a complete census

2. Describe the process of identifying a target population and selecting a sampling frame

3. Compare random sampling and systematic (nonsampling) errors

4. Identify the types of nonprobability sampling, including their advantages and disadvantages

After this lecture, you should be able to

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LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)

5. Summarize the advantages and disadvantages of the various types of probability samples

6. Discuss how to choose an appropriate sample design, as well as challenges for Internet sampling

7. Understand basic statistical terminology8. Interpret frequency distributions, proportions, and

measures of central tendency and dispersion9. Distinguish among population, sample, and

sampling distributions 10. Summarize the use of confidence interval

estimates

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Small Samples Can EnlightenSmall Samples Can Enlighten

““The proof of the pudding is in the The proof of the pudding is in the eating.eating.By By a small sample a small sample we may judge of thewe may judge of thewhole piece.”whole piece.”

Miguel de Cervantes Saavedra Miguel de Cervantes Saavedra authorauthor

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The Nature of SamplingThe Nature of Sampling

PopulationPopulationPopulation ElementPopulation ElementCensusCensusSampleSampleSampling frameSampling frame

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Sampling TerminologySampling Terminology Sample

A subset, or some part, of a larger population.

Population (universe) Any complete group of entities that share

some common set of characteristics. Population Element

An individual member of a population. Census

An investigation of all the individual elements that make up a population.

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Why Sample?Why Sample?

Greater Greater accuracyaccuracy

AvailabiliAvailability of ty of

elementselements

Greater Greater speedspeed

Sampling Sampling providesprovides

Lower Lower costcost

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What Is a Sufficiently What Is a Sufficiently Large Sample?Large Sample?

““In recent Gallup ‘Poll on polls,’ . . . When asked In recent Gallup ‘Poll on polls,’ . . . When asked about the scientific sampling foundation on which about the scientific sampling foundation on which polls are based . . . most said that a survey of polls are based . . . most said that a survey of 1,500 – 2,000 respondents—a larger than average 1,500 – 2,000 respondents—a larger than average sample size for national polls—cannot represent sample size for national polls—cannot represent the views of all Americans.”the views of all Americans.”

Frank Newport Frank Newport The Gallup Poll editor in chiefThe Gallup Poll editor in chief

The Gallup OrganizationThe Gallup Organization

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When Is a Census When Is a Census Appropriate?Appropriate?

NecessaryNecessaryFeasibleFeasible

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What Is a Valid Sample?What Is a Valid Sample?

AccurateAccurate PrecisePrecise

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Why Sample?Why Sample? Pragmatic Reasons

Budget and time constraints. Limited access to total population.

Accurate and Reliable Results Samples can yield reasonably accurate

information.information. Strong similarities Strong similarities in population elements makes in population elements makes

sampling possible.sampling possible. Sampling may be Sampling may be more accurate more accurate than a census.than a census.

Destruction of Test UnitsDestruction of Test Units Sampling Sampling reduces the costs reduces the costs of research in finite of research in finite

populations.populations.

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A Photographic Example of How Sampling WorksA Photographic Example of How Sampling Works

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16–16

Stages in Stages in the the

SelectionSelectionof a of a

SampleSample

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Types of Sampling DesignsTypes of Sampling DesignsElement Selection

Probability Nonprobability

•UnrestrictedUnrestricted • Simple randomSimple random • ConvenienceConvenience

•RestrictedRestricted • Complex randomComplex random • PurposivePurposive

• SystematicSystematic • JudgmentJudgment

•ClusterCluster •QuotaQuota

•StratifiedStratified •SnowballSnowball

•DoubleDouble

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Steps in Sampling DesignSteps in Sampling Design

What is the target What is the target population?population?

What are the parameters What are the parameters of interest?of interest?

What is the sampling What is the sampling frame?frame?

What is the What is the appropriate sampling appropriate sampling

method?method?What size sample is What size sample is

needed?needed?

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When to Use Larger Sample?When to Use Larger Sample?

Desired Desired precisioprecisio

nn

Number Number of of

subgroupsubgroupss

ConfidenConfidence levelce level

PopulatioPopulation n

variancevariance

Small Small error error rangerange

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Practical Sampling ConceptsPractical Sampling Concepts Defining the Target Population

Once the decision to sample has been made, the first question concerns identifying the target population.

What is the relevant population? In many cases this is easy to answer, but in other cases, the decision may be difficult.

At the outset of the sampling process it is vitally important to carefully define the target population so that the proper source from which the data are to be collected can be identified.

To implement the sample in the field, tangible characteristics (e.g. age, gender etc) should be used to define the population.

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Practical Sampling Concepts Practical Sampling Concepts (cont’d)(cont’d)

The Sampling Frame In practice, the sample will be drawn from a

list of population elements that often differs somewhat from the defined target population.

A sampling frame is a list of elements from which the sample may be drawn.

The sampling frame is also called the working population, because these units will eventually provide units involved in the analysis.

The discrepancy between the definition of the population and a sampling frame is the first potential source of error associated with sample selection.

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ExampleExample Target population: Students in

Malaysia between 18 years old and 22 years old.

Sampling frame: students from a higher education institution.

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Practical Sampling Concepts Practical Sampling Concepts (cont’d)(cont’d)

The Sampling Frame A sampling frame error occurs when

certain sample elements are excluded or when the entire population is not accurately represented in the sampling frame.

Population elements can be either under- or overrepresented in a sampling frame.

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Sampling UnitsSampling Units Sampling Unit

A single element or group of elements subject to selection in the sample.

Primary Sampling Unit (PSU) A unit selected in the first stage of sampling.

Secondary Sampling Unit A unit selected in the second stage of

sampling. Tertiary Sampling Unit

A unit selected in the third stage of sampling.

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EXAMPLETarget population: Students in Malaysia between 18 years old and 22 years old.Sample frame: students from a higher education institution.Sampling units:

Advanced Diploma students only (primary sampling unit)

School of Business Studies only (secondary sampling unit)

ABU only (tertiary sampling unit)

16–25

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Random Sampling and Random Sampling and Nonsampling ErrorsNonsampling Errors

If a difference exists between the value of a sample statistic of interest and the value of the corresponding population parameter, a statistical error has occurred.

Two basic causes of differences between statistics and parameters: random sampling errors systematic (nonsampling) errors

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Random Sampling and Nonsampling Errors (cont’d)Random Sampling and Nonsampling Errors (cont’d)

Random Sampling Error Random sampling error is the difference between the

sample result and the result of a census conducted using identical procedures.

Random sampling error occurs because of chance variation in the scientific selection of sampling units.

Because random sampling errors follow chance variations, they tend to cancel one another out when averaged.

This means that properly selected samples are generally good approximations of the population.

Random sampling error is a function of sample size. As sample size increases, random sampling error

decreases It is possible to estimate the random sampling error that

may be expected with various sample sizes.

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Random Sampling and Random Sampling and Nonsampling Errors (cont’d)Nonsampling Errors (cont’d)

Systematic Sampling Error Systematic (nonsampling) errors result

from nonsampling factors, primarily the nature of a study’s design and the correctness of execution.

These errors are not due to chance fluctuations.

Sample biases account for a large portion of errors in research.

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Random Sampling and Random Sampling and Nonsampling Errors (cont’d)Nonsampling Errors (cont’d)

Less than Perfectly Representative Samples Random sampling errors and systematic

errors associated with the sampling process may combine to yield a sample that is less than perfectly representative of the population.

Additional errors will occur if individuals refuse to be interviewed or cannot be contacted.

Such nonresponse error may also cause the sample to be less than perfectly representative.

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EXHIBIT 16.EXHIBIT 16.44 Errors Associated with SamplingErrors Associated with Sampling

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Probability versus Probability versus Nonprobability Sampling Nonprobability Sampling

Several alternative ways to take Several alternative ways to take a sample are available.a sample are available.

The main alternative sampling The main alternative sampling plans may be grouped into two plans may be grouped into two categories:categories: 1. probability techniques1. probability techniques 2. nonprobability techniques.2. nonprobability techniques.

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Probability versus Nonprobability SamplingProbability versus Nonprobability Sampling (cont’d) (cont’d)

Probability Sampling In probability sampling, every element in

the population has a known, nonzero probability of selection.

The simple random sample, in which each member of the population has an equal probability of being selected, is the best-known probability sample.

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Probability versus Nonprobability Probability versus Nonprobability Sampling (cont’d)Sampling (cont’d)

Nonprobability sampling In nonprobability sampling, the probability of any

particular member of the population being chosen is unknown.

The selection of sampling units in nonprobability sampling is quite arbitrary, as researchers rely heavily on personal judgment.

Technically, no appropriate statistical techniques exist for measuring random sampling error from a nonprobability sample.

Therefore, projecting the data beyond the sample is technically speaking, statistically inappropriate.

Nevertheless, nonprobability samples are pragmatic and are used in business research.

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Nonprobability SamplesNonprobability Samples

CostCost

FeasibilFeasibilityity

TimeTime

No need No need to to

generalizgeneralizee Limited Limited

objectiveobjectivess

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Nonprobability Nonprobability Sampling MethodsSampling Methods

ConvenienceConvenienceJudgmentJudgment

QuotaQuotaSnowballSnowball

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Nonprobability Sampling Nonprobability Sampling MethodsMethods

Convenience Sampling Obtaining those people or units that are most

conveniently available. Mall interception survey is applying this

method.

Judgment (Purposive) Sampling An experienced individual selects the sample

based on personal judgment about some appropriate characteristic of the sample member.

E.g. Consumer Price Index (CPI)

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Nonprobability Sampling (cont’d)Nonprobability Sampling (cont’d) Quota Sampling

Ensures that various subgroups of a population will be represented on pertinent characteristics to the exact extent that the investigator desires.

E.g. SOT – 20, SBS - 30 Possible Sources Of Bias

Respondents chosen because they were: Similar to interviewer Easily found Willing to be interviewed Middle-class

Advantages of Quota Sampling Speed of data collection Lower costs Convenience

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Nonprobability Sampling Nonprobability Sampling (cont’d)(cont’d)

Snowball Sampling A sampling procedure in which initial

respondents are selected by probability methods and additional respondents are obtained from information provided by the initial respondents.

E.g. 1 respondent (selected through probability method) recommended another 5 respondents; then the 5 additional respondents recommended another 25 respondents.

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Probability SamplingProbability Sampling Simple Random Sampling

Simple random sampling is a sampling procedure that assures that each element in the population will have an equal chance of being included in the sample.

Drawing names from a hat is a typical example of simple random sampling; each person has an equal chance of being selected.

To use this method, we must have a list of all members in a population, then we draw lots.

Systematic Sampling A starting point is selected by a random process

and then every nth number on the list is selected. E.g. for the list of all members in a population,

every 10th name will be selected.

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14-40

Simple RandomSimple Random

AdvantagesAdvantages•Easy to implement Easy to implement with random dialingwith random dialing

DisadvantagesDisadvantages•Requires list of Requires list of population elementspopulation elements•Time consumingTime consuming•Larger sample Larger sample neededneeded•Produces larger Produces larger errorserrors•High costHigh cost

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SystematicSystematic

AdvantagesAdvantages•Simple to designSimple to design•Easier than simple Easier than simple randomrandom•Easy to determine Easy to determine sampling distribution sampling distribution of mean or proportionof mean or proportion

DisadvantagesDisadvantages•Periodicity within Periodicity within population may skew population may skew sample and resultssample and results•Trends in list may Trends in list may bias resultsbias results•Moderate costModerate cost

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Proportional versus Disproportional Proportional versus Disproportional SamplingSampling Stratified Sampling

Simple random subsamples that are more or less equal on some characteristic are drawn from within each stratum (subgroup) of the population.

E.g. based on the same characteristics, we divide students into 3 subgroups (e.g. students with straight-pass, students with re-sit units, students with repeat units), then we use simple random sampling method to draw a subsample.

Proportional Stratified Sample The number of sampling units drawn from each stratum

is in proportion to the population size of that stratum. Disproportional Stratified Sample

The sample size for each stratum is allocated according to analytical considerations.

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EXHIBIT 16.EXHIBIT 16.55 Disproportional Sampling: Hypothetical ExampleDisproportional Sampling: Hypothetical Example

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14-44

StratifiedStratified

AdvantagesAdvantages•Control of sample size in Control of sample size in stratastrata•Increased statistical Increased statistical efficiencyefficiency•Provides data to Provides data to represent and analyze represent and analyze subgroupssubgroups•Enables use of different Enables use of different methods in stratamethods in strata

DisadvantagesDisadvantages•Increased error if Increased error if subgroups are selected at subgroups are selected at different ratesdifferent rates•Especially expensive if Especially expensive if strata on population must strata on population must be created be created •High costHigh cost

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Cluster SamplingCluster Sampling The purpose of cluster sampling is to sample

economically while retaining the characteristics of a probability sample.

In a cluster sample, the primary sampling unit is no longer the individual element in the population (e.g., grocery stores) but a larger cluster of elements located in proximity to one another (e.g., cities).

Cluster sampling is classified as a probability sampling technique because of either the random selection of clusters or the random selection of elements within each cluster.

Cluster samples frequently are used when lists of the sample population are not available.

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EXHIBIT 16.EXHIBIT 16.66 Examples of ClustersExamples of Clusters

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Cluster Cluster

AdvantagesAdvantages•Provides an unbiased Provides an unbiased estimate of population estimate of population parameters if properly parameters if properly donedone•Economically more Economically more efficient than simple efficient than simple randomrandom•Lowest cost per sampleLowest cost per sample•Easy to do without listEasy to do without list

DisadvantagesDisadvantages•Often lower statistical Often lower statistical efficiency due to efficiency due to subgroups being subgroups being homogeneous rather than homogeneous rather than heterogeneousheterogeneous•Moderate costModerate cost

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Multistage Area SamplingMultistage Area Sampling Multistage Area Sampling

Involves using a combination of two or more probability sampling techniques.

Typically, geographic areas are randomly selected in progressively smaller (lower-population) units.

Researchers may take as many steps as necessary to achieve a representative sample.

Progressively smaller geographic areas are chosen until a single housing unit is selected for interviewing.

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EXHIBIT 16.EXHIBIT 16.88 Geographic Hierarchy Inside Urbanized AreasGeographic Hierarchy Inside Urbanized Areas

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14-50

Stratified and Cluster SamplingStratified and Cluster Sampling

StratifiedStratified•Population divided into Population divided into few subgroupsfew subgroups•Homogeneity within Homogeneity within subgroupssubgroups•Heterogeneity between Heterogeneity between subgroupssubgroups•Choice of elements Choice of elements from within each from within each subgroupsubgroup

ClusterCluster•Population divided into Population divided into many subgroupsmany subgroups•Heterogeneity within Heterogeneity within subgroupssubgroups•Homogeneity between Homogeneity between subgroupssubgroups•Random choice of Random choice of subgroups subgroups

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14-51

Area SamplingArea Sampling

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Double SamplingDouble Sampling

AdvantagesAdvantages•May reduce costs if May reduce costs if first stage results in first stage results in enough data to stratify enough data to stratify or cluster the or cluster the populationpopulation

DisadvantagesDisadvantages•Increased costs if Increased costs if discriminately useddiscriminately used

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What Is the Appropriate What Is the Appropriate Sample Design? (cont’d)Sample Design? (cont’d)

Resources The cost associated with the different

sampling techniques varies tremendously. If the researcher’s financial and human

resources are restricted, certain options will have to be eliminated.

Managers concerned with the cost of the research versus the value of the information often will opt for cost savings from a certain nonprobability sample design rather than make the decision to conduct no research at all.

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What Is the Appropriate Sample What Is the Appropriate Sample Design? (cont’d)Design? (cont’d)

Time Researchers who need to meet a deadline or

complete a project quickly will be more likely to select simple, less time-consuming sample designs.

Advance Knowledge of the Population In many cases, a list of population elements

will not be available to the researcher. A lack of adequate lists lack of adequate lists may automatically rule

out systematic sampling, stratified sampling, or other sampling designs, or it may dictate that a preliminary study, such as a short telephone survey using random digit dialing, be conducted to generate information to build a sampling frame for the primary study.

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What Is the Appropriate What Is the Appropriate Sample Design? (cont’d)Sample Design? (cont’d)

National versus Local Project Geographic proximity of population

elements will influence sample design. When population elements are unequally

distributed geographically, a cluster sample may become much more attractive.

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© 2010 South-Western/Cengage Learning. All rights reserved. May not

be scanned, copied or duplicated, or posted to a publically accessible

website, in whole or in part.16–56

EXHIBIT 16.EXHIBIT 16.99 Comparison of Sampling Techniques: Nonprobability SamplesComparison of Sampling Techniques: Nonprobability Samples

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© 2010 South-Western/Cengage Learning. All rights reserved. May not

be scanned, copied or duplicated, or posted to a publically accessible

website, in whole or in part.16–57

EXHIBIT 16.EXHIBIT 16.1010 Comparison of Sampling Techniques: Probability SamplesComparison of Sampling Techniques: Probability Samples

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Determination of sample sizeDetermination of sample size Descriptive and Inferential Statistics

There are two applications of statistics: (1) to describe characteristics of the

population or sample (descriptive statistics) and

(2) to generalize from the sample to the population (inferential statistics).

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Sample Statistics and Population Sample Statistics and Population ParametersParameters

The primary purpose of inferential statistics is to make a judgment about the population, or the collection of all elements about which one seeks information.

The sample is a subset or relatively small fraction of the total number of elements in the population.

Sample statistics are variables in the sample or measures computed from the sample data.

Population parameters are variables or measured characteristics of the population.

We will generally use Greek lowercase letters to denote population parameters (e.g., μ or σ) and English letters to denote sample statistics (e.g., X or S).

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Making Data UsableMaking Data Usable To make data usable, this information

must be organized and summarized. Methods for doing this include:

frequency distributionsproportionsmeasures of central tendency

and dispersion

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Making Data Usable (cont’d)Making Data Usable (cont’d) Frequency Distributions

Constructing a frequency table or frequency distribution is one of the most common means of summarizing a set of data.

The frequency of a value is the number of times a particular value of a variable occurs.

Exhibit 17.1 represents a frequency distribution of respondents’ answers to a question asking how much customers had deposited in the savings and loan.

It is also quite simple to construct a distribution of relative frequency, or a percentage distribution, which is developed by dividing the frequency of each

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EXHIBIT 17.EXHIBIT 17.11 Frequency Distribution of DepositsFrequency Distribution of Deposits

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EXHIBIT 17.EXHIBIT 17.22 Percentage Distribution of DepositsPercentage Distribution of Deposits

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EXHIBIT 17.EXHIBIT 17.33 Probability Distribution of DepositsProbability Distribution of Deposits

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Population Mean

Making Data Usable (cont’d)Making Data Usable (cont’d) Proportion

The percentage of elements that meet some criterion

Measures of Central Tendency Mean: the arithmetic average. Median: the midpoint; the value below

which half the values in a distribution fall. Mode: the value that occurs most often.

Sample Mean

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EXHIBIT 17.EXHIBIT 17.44 Number of Sales Calls per Day by SalespersonNumber of Sales Calls per Day by Salesperson

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EXHIBIT 17.EXHIBIT 17.55 Sales Levels for Two Products with Identical Average SalesSales Levels for Two Products with Identical Average Sales

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Measures of DispersionMeasures of DispersionThe Range

The distance between the smallest and the largest values of a frequency distribution.

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EXHIBIT 17.EXHIBIT 17.66 Low Dispersion versus High DispersionLow Dispersion versus High Dispersion

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Measures of Dispersion (cont’d)Measures of Dispersion (cont’d) Why Use the Standard Deviation?

Variance A measure of variability or dispersion. Its square root is the standard deviation.

Standard deviation A quantitative index of a distribution’s spread, or

variability; the square root of the variance for a distribution.

The average of the amount of variance for a distribution.

Used to calculate the likelihood (probability) of an event occurring.

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Calculating Deviation Calculating Deviation

Standard Deviation =

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EXHIBIT 17.EXHIBIT 17.77 Calculating a Standard Deviation: Number of Sales Calls per Day for Eight Calculating a Standard Deviation: Number of Sales Calls per Day for Eight SalespeopleSalespeople

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The Normal DistributionThe Normal Distribution Normal Distribution

A symmetrical, bell-shaped distribution (normal curve) that describes the expected probability distribution of many chance occurrences.

99% of its values are within ± 3 standard deviations from its mean.

Example: IQ scores Standardized Normal Distribution

A purely theoretical probability distribution that reflects a specific normal curve for the standardized value, z.

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EXHIBIT 17.EXHIBIT 17.88 Normal Distribution: Distribution of Intelligence Quotient (IQ) ScoresNormal Distribution: Distribution of Intelligence Quotient (IQ) Scores

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The Normal Distribution (cont’d)The Normal Distribution (cont’d) Characteristics of a Standardized Normal

Distribution1. It is symmetrical about its mean; the tails on

both sides are equal.2. The mean identifies the normal curve’s highest

point (the mode) and the vertical line about which this normal curve is symmetrical.

3. The normal curve has an infinite number of cases (it is a continuous distribution), and the area under the curve has a probability density equal to 1.0.

4. The standardized normal distribution has a mean of 0 and a standard deviation of 1.

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EXHIBIT 17.EXHIBIT 17.99 Standardized Normal DistributionStandardized Normal Distribution

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The Normal Distribution (cont’d)The Normal Distribution (cont’d) Standardized Values, Z

Used to compare an individual value to the population mean in units of the standard deviation

The standardized normal distribution can be used to translate/transform any normal variable, X, into the standardized value, Z.

Researchers can evaluate the probability of the occurrence of many events without any difficulty.

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EXHIBIT 17.EXHIBIT 17.1010 Standardized Normal Table: Area under Half of the Normal CurveStandardized Normal Table: Area under Half of the Normal Curveaa

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EXHIBIT 17.EXHIBIT 17.1111 Standardized Standardized Values can be Values can be

Computed from Computed from Flat or Peaked Flat or Peaked Distributions Distributions Resulting in a Resulting in a Standardized Standardized Normal CurveNormal Curve

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EXHIBIT 17.12EXHIBIT 17.12 Standardized Distribution CurveStandardized Distribution Curve

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17–81

Population Distribution, Sample Population Distribution, Sample Distribution, and Sampling Distribution, and Sampling

DistributionDistribution Population Distribution

A frequency distribution of the elements of a population.

Sample Distribution A frequency distribution of a sample.

Sampling Distribution A theoretical probability distribution of sample

means for all possible samples of a certain size drawn from a particular population.

Standard Error of the Mean The standard deviation of the sampling

distribution.

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Three Important DistributionsThree Important Distributions

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EXHIBIT 17.EXHIBIT 17.1313Fundamental Fundamental

Types of Types of DistributionsDistributions

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Central-limit TheoremCentral-limit Theorem Central-limit Theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

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© 2010 South-Western/Cengage Learning. All rights reserved. May not

be scanned, copied or duplicated, or posted to a publically accessible

website, in whole or in part.17–85

EXHIBIT 17.14EXHIBIT 17.14The Mean The Mean

Distribution of Distribution of Any Any

Distribution Distribution Approaches Approaches Normal as Normal as n n

IncreasesIncreases

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EXHIBIT 17.15EXHIBIT 17.15 Population Distribution: Hypothetical Product DefectPopulation Distribution: Hypothetical Product Defect

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EXHIBIT 17.16EXHIBIT 17.16 Calculation of Population MeanCalculation of Population Mean

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EXHIBIT 17.17EXHIBIT 17.17 Arithmetic Arithmetic Means of Means of

Samples and Samples and Frequency Frequency Distribution Distribution of Sample of Sample

MeansMeans

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Estimation of Parameters and Confidence Estimation of Parameters and Confidence Intervals (for inference statistics)Intervals (for inference statistics)

Point Estimates An estimate of the population mean in the form

of a single value, usually the sample mean. Gives no information about the possible magnitude of

random sampling error. Confidence Interval Estimate

A specified range of numbers within which a population mean is expected to lie.

An estimate of the population mean based on the knowledge that it will be equal to the sample mean plus or minus a small sampling error.

i.e. μ = X + a small sampling error.

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The information can be used to estimate market demand. E.g. with 95 percent confidence, the

average number of unit used per week is between 2.3 and 2.9.

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Confidence IntervalsConfidence Intervals Confidence Level

A percentage or decimal value that tells how confident a researcher can be about being correct.

It states the long-run percentage of confidence intervals that will include the true population mean.

The crux of the problem for a researcher is to determine how much random sampling error to tolerate.

Traditionally, researchers have used the 95% confidence level (a 5% tolerance for error).

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Calculating a Confidence Calculating a Confidence IntervalInterval

Estimation of the sampling error

Approximate location (value) of the population mean

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Calculating a Confidence Interval Calculating a Confidence Interval (cont’d)(cont’d)

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Sample SizeSample Size Random Error and Sample Size

Random sampling error varies with samples of different sizes.

Increases in sample size reduce sampling error at a decreasing rate.

Diminishing returns - random sampling error is inversely proportional to the square root of n.

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EXHIBIT 17.18EXHIBIT 17.18 Relationship between Sample Size and ErrorRelationship between Sample Size and Error

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EXHIBIT 17.19EXHIBIT 17.19 Statistical Information Needed to Determine Sample Size for Statistical Information Needed to Determine Sample Size for Questions Involving MeansQuestions Involving Means

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Factors of Concern in Choosing Factors of Concern in Choosing Sample SizeSample Size

Variance (or Heterogeneity) A heterogeneous population has more

variance (a larger standard deviation) which will require a larger sample.

A homogeneous population has less variance (a smaller standard deviation) which permits a smaller sample.

Magnitude of Error (Confidence Interval) How precise must the estimate be?

Confidence Level How much error will be tolerated? For

business research, 95 percent confidence 95 percent confidence level is used.

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Estimating Sample Size for Estimating Sample Size for Questions Involving MeansQuestions Involving Means

Sequential Sampling Conducting a pilot study to estimate the

population parameters so that another, larger sample of the appropriate sample size may be drawn.

Estimating sample size:

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Sample Size ExampleSample Size Example Suppose a survey researcher, studying expenditures

on lipstick, wishes to have a 95 percent confidence level (Z) and a range of error (E) of less than $2.00. The estimate of the standard deviation is $29.00. What is the calculated sample size?

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Sample Size ExampleSample Size Example Suppose, in the same example as the one before,

the range of error (E) is acceptable at $4.00. Sample size is reduced.

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Calculating Sample Size at the Calculating Sample Size at the 99 Percent Confidence Level99 Percent Confidence Level

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Determining Sample Size for ProportionsDetermining Sample Size for Proportions

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Determining Sample Size for Proportions Determining Sample Size for Proportions (cont’d)(cont’d)

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Calculating Example Sample Calculating Example Sample Size at the 95 Percent Size at the 95 Percent

Confidence LevelConfidence Level

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EXHIBIT 17.20EXHIBIT 17.20 Selected Tables for Determining Sample Size When the Characteristic of Selected Tables for Determining Sample Size When the Characteristic of Interest Is a ProportionInterest Is a Proportion

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EXHIBIT 17.21EXHIBIT 17.21 Allowance for Random Sampling Error (Plus and Minus Percentage Allowance for Random Sampling Error (Plus and Minus Percentage Points) at 95 Percent Confidence LevelPoints) at 95 Percent Confidence Level

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The Nature of FieldworkThe Nature of Fieldwork Fieldworker

An individual who is responsible for gathering data in the field.

Typical fieldwork activities: Administering a questionnaire door to door Telephone interview calling from a central

location Counting pedestrians in a shopping mall Supervising the collection of data

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Making Initial ContactMaking Initial Contact Personal Interviews

Making opening remarks that will convince the respondent that his or her cooperation is important.

Telephone Interviews Giving the interviewer’s name personalizes the call. Providing the name of the research agency is used

to imply that the caller is trustworthy. Providing an accurate estimate of the time helps

gain cooperation. Internet Surveys

Respondent may receive an e-mail requesting assistance.

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Gaining ParticipationGaining Participation Foot-in-the-Door Compliance Technique

Compliance with large or difficult task is induced by first obtaining the respondent’s compliance with a smaller request.

Door-in-the-Face Compliance Technique A two-step process for securing a high

response rate. Step 1: An initial request, so large that nearly

everyone refuses it, is made. Step 2: A second request is made for a smaller

favour; respondents are expected to comply with this more reasonable request.

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Asking the QuestionsAsking the Questions Major Rules for Asking Questions:

1. Ask questions exactly as they are worded in the questionnaire.

2. Read each question very carefully and clearly.3. Ask the questions in the specified order.4. Ask every question specified in the

questionnaire.5. Repeat questions that are misunderstood or

misinterpreted.

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Probing When No Response Is Probing When No Response Is GivenGiven

Probing Verbal attempts made by a field-worker when

the respondent must be motivated to communicate his or her answers more fully.

Probing Tactics that Enlarge and Clarify: Repeating the question Using a silent probe Repeating the respondent’s reply Asking a neutral question

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EXHIBIT 18.EXHIBIT 18.11 Commonly Used Probes and Their AbbreviationsCommonly Used Probes and Their Abbreviations

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Recording the ResponsesRecording the Responses Rules for recording responses to fixed-alternative

questions vary with the specific questionnaire. Rules for recording open-ended answers include:

Record 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.

How answers are recorded can affect researchers’ interpretation of the respondent’s answers.

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18–114

EXHIBIT 18.EXHIBIT 18.22 A Completed Portion of a Response Form with NotesA Completed Portion of a Response Form with Notes

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Terminating the InterviewTerminating the Interview How to close the interview is important:

Fieldworkers should wait to close the interview until they have secured all pertinent information including spontaneous comments of the respondent.

Fieldworkers should answer any respondent questions concerning the nature and purpose of the study to the best of his or her ability.

Avoiding hasty departures is a matter of courtesy.

It is important to thank the respondent for his or her time and cooperation as reinterviewing may be required.

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Principles of Good InterviewingPrinciples of Good Interviewing

The Basics:1. Have integrity, and be honest.2. Have patience and tact.3. Pay attention to accuracy and detail.4. Exhibit a real interest in the inquiry at hand,

but keep your own opinions to yourself.5. Be a good listener.6. Keep the inquiry and respondents’ responses

confidential.7. Respect others’ rights.

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Principles of Good Principles of Good Interviewing (cont’d)Interviewing (cont’d)

Required Practices1. Complete the number of interviews according to the

sampling plan assigned to you.2. Follow the directions provided.3. Make every effort to keep schedules.4. Keep control of each interview you do.5. Complete the questionnaires meticulously.6. Check over each questionnaire you have completed.7. Compare your sample execution and assigned quota with the

total number of questionnaires you have completed.8. Clear up any questions with the research agency.

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Further ReadingFurther Reading COOPER, D.R. AND SCHINDLER, P.S. (2011)

BUSINESS RESEARCH METHODS, 11TH EDN, MCGRAW HILL

ZIKMUND, W.G., BABIN, B.J., CARR, J.C. AND GRIFFIN, M. (2010) BUSINESS RESEARCH METHODS, 8TH EDN, SOUTH-WESTERN

SAUNDERS, M., LEWIS, P. AND THORNHILL, A. (2012) RESEARCH METHODS FOR BUSINESS STUDENTS, 6TH EDN, PRENTICE HALL.

SAUNDERS, M. AND LEWIS, P. (2012) DOING RESEARCH IN BUSINESS & MANAGEMENT, FT PRENTICE HALL.

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DETERMINING SAMPLE SIZEDETERMINING SAMPLE SIZEAPPENDIXAPPENDIX

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14-120

Random SamplesRandom Samples

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14-121

Increasing PrecisionIncreasing Precision

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14-122

Confidence Levels & the Confidence Levels & the Normal CurveNormal Curve

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14-123

Standard ErrorsStandard Errors

Standard Error(Z score)

% of Area Approximate Degree of

Confidence1.00 68.27 68%

1.65 90.10 90%

1.96 95.00 95%

3.00 99.73 99%

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14-124

Central Limit TheoremCentral Limit Theorem

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14-125

Estimates of Dining VisitsEstimates of Dining Visits

Confidence Z score

% of Area

Interval Range (visits per

month)68% 1.00 68.27 9.48-10.52

90% 1.65 90.10 9.14-10.86

95% 1.96 95.00 8.98-11.02

99% 3.00 99.73 8.44-11.56

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14-126

Calculating Sample Size for Calculating Sample Size for Questions involving MeansQuestions involving Means

Precision

Confidence level

Size of interval estimate

Population DispersionNeed for FPA

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14-127

Metro U Sample Size for MeansMetro U Sample Size for Means

Steps InformationInformationDesired confidence level 95% (z = 1.96)95% (z = 1.96)

Size of the interval estimate .5 meals per month.5 meals per monthExpected range in

population0 to 30 meals0 to 30 meals

Sample mean 1010Standard deviation 4.14.1

Need for finite population adjustment

NoNo

Standard error of the mean .5/1.96 = .255.5/1.96 = .255Sample size (4.1)(4.1)22/ (.255)/ (.255)22 = 259 = 259

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14-128

Proxies of the Proxies of the Population DispersionPopulation Dispersion

Previous research on the Previous research on the topictopic

Pilot test or pretestPilot test or pretest Rule-of-thumb calculationRule-of-thumb calculation

1/6 of the range1/6 of the range

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14-129

Metro U Sample Size for Metro U Sample Size for ProportionsProportions

Steps InformationInformationDesired confidence level 95% (z = 1.96)95% (z = 1.96)

Size of the interval estimate .10 (10%).10 (10%)Expected range in population 0 to 100%0 to 100%Sample proportion with given

attribute30%30%

Sample dispersion Pq = .30(1-.30) = .21Pq = .30(1-.30) = .21Finite population adjustment NoNo

Standard error of the proportion

.10/1.96 = .051.10/1.96 = .051

Sample size .21/ (.051).21/ (.051)22 = 81 = 81

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14-130

Random SamplesRandom Samples

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14-131

Confidence LevelsConfidence Levels

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14-132

Metro U. Dining Club StudyMetro U. Dining Club Study