Copyright © 2008 by Nelson, a division of Thomson Canada Limited Chapter 17 Part 5 Analysis and Interpretation of Data BASIC DATA ANALYSIS.

Copyright © 2008 by Nelson, a division of Thomson Canada Limited

Chapter

17

Part 5

Analysis and Interpretation of Data

BASIC DATA ANALYSIS

LEARNING OBJECTIVESLEARNING OBJECTIVESLEARNING OBJECTIVESLEARNING OBJECTIVES

1. To understand that analysis consists of summarizing, rearranging, ordering, or manipulating data

2. To compute and explain the purposes of simple tabulations and cross-tabulations

3. To use cross-tabulation procedures to discuss the relationship between two variables

4. To discuss the nature of data transformations

5. To explain how to summarize rank-order data

6. To describe some computer software designed for descriptive analysis

What you will learn in this chapter

Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–1

LEARNING OBJECTIVES (cont’d)LEARNING OBJECTIVES (cont’d)LEARNING OBJECTIVES (cont’d)LEARNING OBJECTIVES (cont’d)

7. To define hypothesis, null hypothesis, alternative hypothesis, and significance level

8. To discuss the steps in the hypothesis-testing procedure

9. To describe the factors that influence the choice of statistical method to use for analysis

What you will learn in this chapter


• Descriptive AnalysisDescriptive AnalysisThe transformation of raw data into a form that will

make them easy to understand and interpret; rearranging, ordering, and manipulating data to generate descriptive information

The Nature of Descriptive AnalysisThe Nature of Descriptive AnalysisThe Nature of Descriptive AnalysisThe Nature of Descriptive Analysis


• TabulationTabulationThe orderly arrangement of data in a table or other

summary formatFrequency table

The arrangement of statistical data in a row-and-column format that exhibits the count of responses or observations for each category assigned to a variable

• PercentagesPercentagesWhether data are tabulated by computer or by hand,

percentages, cumulative percentages, and frequency distributions are useful

TabulationTabulationTabulationTabulation


• Measures of Central TendencyMeasures of Central TendencyDescribing central tendencies of the distribution with

the mean, median, or mode is another basic form of descriptive analysis

These measures are most useful when the purpose is to identify typical values of a variable or the most common characteristic of a group

Tabulation (cont’d)Tabulation (cont’d)Tabulation (cont’d)Tabulation (cont’d)


• Cross-TabulationCross-TabulationOrganizing data by groups, categories, or classes to

facilitate comparisons; a joint frequency distribution of observations on two or more sets of variables

• Two-Way (Contingency) TablesTwo-Way (Contingency) TablesThe results of a cross-tabulation of two variables,

such as answers to two survey questions

• Percentage Cross-TabulationsPercentage Cross-TabulationsBase

The number of respondents or observations (in a row or column) used as a basis for computing percentages

Cross-TabulationCross-TabulationCross-TabulationCross-Tabulation


• Elaboration and RefinementElaboration and RefinementElaboration analysis

An analysis of the basic cross-tabulation for each level of a variable not previously considered, such as subgroups of the sample

Moderator variable A third variable that, when introduced into an analysis,

alters or has a contingent effect on the relationship between an independent variable and a dependent variable

Spurious relationship An apparent relationship between two variables that is not

authentic

Cross-Tabulation (cont’d)Cross-Tabulation (cont’d)Cross-Tabulation (cont’d)Cross-Tabulation (cont’d)


• How Many Cross-Tabulations?How Many Cross-Tabulations?The number of cross-tabulations should be

determined early, when research objectives are stated

Cross-Tabulation (cont’d)Cross-Tabulation (cont’d)Cross-Tabulation (cont’d)Cross-Tabulation (cont’d)


• Data Transformation (Data Conversion)Data Transformation (Data Conversion)The process of changing the original form of data to

a format suitable to achieve the research objective

Data TransformationData TransformationData TransformationData Transformation


• Rank OrderRank Order Respondents often rank order brand preferences or

other variables of interest to researchers. To summarize these data for all respondents, the analyst performs a data transformation by multiplying the frequency by the rank (score) to develop a new scale that represents the summarized rank orders

Calculating Rank OrderCalculating Rank OrderCalculating Rank OrderCalculating Rank Order


• TablesTablesTables are most useful for presenting numerical

information, especially when several pieces of information have been gathered about each item discussed

The purpose of each table is to facilitate the summarization and communication of the data’s meaning

Tabular and Graphic Methods of Displaying Tabular and Graphic Methods of Displaying DataDataTabular and Graphic Methods of Displaying Tabular and Graphic Methods of Displaying DataData


• Charts and GraphsCharts and GraphsCharts translate numerical information into visual

form so that relationships may be easily grasped

• Pie ChartsPie ChartsPie charts shows the composition of some total

quantity at a particular time

• Line GraphsLine GraphsLine graphs are useful for showing the relationship of

one variable to another

Tabular and Graphic Methods of Displaying Tabular and Graphic Methods of Displaying Data (cont’d)Data (cont’d)Tabular and Graphic Methods of Displaying Tabular and Graphic Methods of Displaying Data (cont’d)Data (cont’d)


• Bar ChartsBar ChartsBar charts show changes in the value of a

dependent variable (plotted on the vertical axis) at discrete intervals of the independent variable (on the horizontal axis)

Tabular and Graphic Methods of Displaying Tabular and Graphic Methods of Displaying Data (cont’d)Data (cont’d)Tabular and Graphic Methods of Displaying Tabular and Graphic Methods of Displaying Data (cont’d)Data (cont’d)


SASStatistical Package for the Social Sciences (SPSS)STATAMINITAB

Computer Programs for AnalysisComputer Programs for AnalysisComputer Programs for AnalysisComputer Programs for Analysis


• What is a Hypothesis?What is a Hypothesis?Hypothesis

An unproven proposition or supposition that tentatively explains certain facts or phenomena; a proposition that is empirically testable

• Null and Alternative HypothesisNull and Alternative HypothesisNull Hypothesis

A statement about a status quo asserting that any change from what has been thought to be true will be due entirely to random sampling error

Alternative Hypothesis A statement indicating the opposite of the null hypothesis

Univariate Statistics: Stating a HypothesisUnivariate Statistics: Stating a HypothesisUnivariate Statistics: Stating a HypothesisUnivariate Statistics: Stating a Hypothesis


• The Hypothesis-Testing ProcedureThe Hypothesis-Testing ProcedureThe specifically stated hypothesis is derived from the

research objectivesA sample is obtained and the relevant variable is

measuredThe measured sample value is compared to the

value either stated explicitly or implied in the hypothesis

Significance level The critical probability in choosing between the null and

alternative hypotheses; the probability level that is too low to warrant support of the null hypothesis

Hypothesis TestingHypothesis TestingHypothesis TestingHypothesis Testing


• An Example of Hypothesis TestingAn Example of Hypothesis TestingCritical values

The values that lie exactly on the boundary of the region of rejection

Example of hypothesis testingThe null hypothesis: the mean is equal to 3.0:

Ho : μ = 3.0

The alternative hypothesis: the mean is not equal to 3.0: H1 : μ ≠ 3.0

Hypothesis Testing (cont’d)Hypothesis Testing (cont’d)Hypothesis Testing (cont’d)Hypothesis Testing (cont’d)


• An Example of Hypothesis Testing (cont’d)An Example of Hypothesis Testing (cont’d)

Hypothesis Testing (cont’d)Hypothesis Testing (cont’d)Hypothesis Testing (cont’d)Hypothesis Testing (cont’d)


• Chi-Square (Chi-Square (χχ22) Test) TestA hypothesis test that allows for investigation of

statistical significance in the analysis of a frequency distribution

Example of chi-square test

where

χ² = chi-square statistics

Oi = observed frequency in the ith cell

Ei = expected frequency on the ith cell

The Chi-Square Test for Goodness of FitThe Chi-Square Test for Goodness of FitThe Chi-Square Test for Goodness of FitThe Chi-Square Test for Goodness of Fit


i

ii( ²

E

E )²O

• Chi-Square (Chi-Square (χχ22) Test (cont’d)) Test (cont’d) Example of chi-square test (cont’d)

The Chi-Square Test for Goodness of Fit The Chi-Square Test for Goodness of Fit (cont’d)(cont’d)The Chi-Square Test for Goodness of Fit The Chi-Square Test for Goodness of Fit (cont’d)(cont’d)


Awareness of Tire Manufacturer’s Brand

AwareUnaware

Frequency

6040

100

Brand Awareness

Aware

Unaware

Total

• Number of VariablesNumber of VariablesThe researcher conducts univariate statistical

analysis when attempting to generalize from a sample about one variable at a time

Statistically describing the relationship between two variables at one time requires bivariate statistical analysis

Choosing the Appropriate TechniqueChoosing the Appropriate TechniqueChoosing the Appropriate TechniqueChoosing the Appropriate Technique


• Scale of MeasurementScale of MeasurementThe scale of measurement on which the data are

based or the type of measurement reflected in the data determines the permissible statistical techniques and appropriate empirical operations to perform

Choosing the Appropriate Technique (cont’d)Choosing the Appropriate Technique (cont’d)Choosing the Appropriate Technique (cont’d)Choosing the Appropriate Technique (cont’d)


• Type of Question to be AnsweredType of Question to be AnsweredThe type of question the researcher is

attempting to answer is a consideration in the choice of statistical technique

Marketing researchers frequently question whether a mean, a proportion, or a distribution differs from what was expected

Two other frequently asked questions are: Are there differences between two (or more)

groups, and Is there a relationship between two or more

variables?

Choosing the Appropriate Technique (cont’d)Choosing the Appropriate Technique (cont’d)Choosing the Appropriate Technique (cont’d)Choosing the Appropriate Technique (cont’d)


Copyright © 2008 by Nelson, a division of Thomson Canada Limited Chapter 17 Part 5 Analysis and Interpretation of Data BASIC DATA ANALYSIS.

Documents

basic crosstabulation

crosstabulation contdhow

crosstabulation procedures

tabulationorganizing

descriptive analysiswhat

alternative hypothesis

null hypothesis

independent variable