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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
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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
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• 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
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• 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
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• 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)
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• 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
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• 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)
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• 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)
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• 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
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• 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
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• 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
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• 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)
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• 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)
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SASStatistical Package for the Social Sciences (SPSS)STATAMINITAB
Computer Programs for AnalysisComputer Programs for AnalysisComputer Programs for AnalysisComputer Programs for Analysis
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• 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
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• 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
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• 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)
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• 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)
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• 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
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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)
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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
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• 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)
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• 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)
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