1. BUSINESS MARKET RESEARCH
ZIKMUND BABIN
CARR GRIFFIN
BUSINESS MARKET RESEARCH
EIGHTH EDITION

2. LEARNING OUTCOMES After studying this chapter, you should be able to
Recognize when a bivariate statistical test is appropriate
Calculate and interpret a χ2 test for a contingency table
Calculate and interpret an independent samples t-test comparing two means
Understand the concept of analysis of variance (ANOVA)
Interpret an ANOVA table
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3. What Is the Appropriate Test of Difference?
Test of Differences
An investigation of a hypothesis that two (or more) groups differ with respect to measures on a variable.
Behavior, characteristics, beliefs, opinions, emotions, or attitudes
Bivariate Tests of Differences
Involve only two variables: a variable that acts like a dependent variable and a variable that acts as a classification variable.
Differences in mean scores between groups or in comparing how two groups’ scores are distributed across possible response categories.
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4. EXHIBIT 22.1 Some Bivariate Hypotheses
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5. Cross-Tabulation Tables: The χ2 Test for Goodness-of-Fit
Cross-Tabulation (Contingency) Table
A joint frequency distribution of observations on two more variables.
χ2 Distribution
Provides a means for testing the statistical significance of a contingency table.
Involves comparing observed frequencies (Oi) with expected frequencies (Ei) in each cell of the table.
Captures the goodness- (or closeness-) of-fit of the observed distribution with the expected distribution.
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6. Chi-Square Test χ² = chi-square statistic
Oi = observed frequency in the ith cell
Ei = expected frequency on the ith cell
Ri = total observed frequency in the ith row
Cj = total observed frequency in the jth column
n = sample size
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7. Degrees of Freedom (d.f.)
d.f.=(R-1)(C-1)
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8. Example: Papa John’s Restaurants
Univariate Hypothesis: Papa John’s restaurants are more likely to be located in a stand-alone location or in a shopping center.
Bivariate Hypothesis: Stand-alone locations are more likely to be profitable than are shopping center locations.
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9. Example: Papa John’s Restaurants (cont’d)
In this example, χ2 = with 1 d.f.
From Table A.4, the critical value at the 0.05 level with 1 d.f. is 3.84.
Thus, we are 95 percent confident that the observed values do not equal the expected values.
But are the deviations from the expected values in the hypothesized direction?
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10. χ2 Test for Goodness-of-Fit Recap
Testing the hypothesis involves two key steps:
Examine the statistical significance of the observed contingency table.
Examine whether the differences between the observed and expected values are consistent with the hypothesized prediction.
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11. The t-Test for Comparing Two Means
Independent Samples t-Test
A test for hypotheses stating that the mean scores for some interval- or ratio-scaled variable grouped based on some less-than-interval classificatory variable are not the same.
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12. The t-Test for Comparing Two Means (cont’d)
Pooled Estimate of the Standard Error
An estimate of the standard error for a t-test of independent means that assumes the variances of both groups are equal.
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13. EXHIBIT 22.2 Independent Samples t-Test Results
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14. EXHIBIT 22.3 SAS t-Test Output
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15. Comparing Two Means (cont’d)
Paired-Samples t-Test
Compares the scores of two interval variables drawn from related populations.
Used when means need to be compared that are not from independent samples.
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16. EXHIBIT 22.4 Example Results for a Paired Samples t-Test
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17. The Z-Test for Comparing Two Proportions
Z-Test for Differences of Proportions
Tests the hypothesis that proportions are significantly different for two independent samples or groups.
Requires a sample size greater than thirty.
The hypothesis is: Ho: π1 = π2 may be restated as: Ho: π1 - π2 = 0
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18. The Z-Test for Comparing Two Proportions
Z-Test statistic for differences in large random samples:
p1 = sample portion of successes in Group 1
p2 = sample portion of successes in Group 2
(p1 - p1) = hypothesized population proportion 1
minus hypothesized population proportion 2
Sp1-p2 = pooled estimate of the standard errors of differences of proportions
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19. The Z-Test for Comparing Two Proportions
To calculate the standard error of the differences in proportions:
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20. One-Way Analysis of Variance (ANOVA)
An analysis involving the investigation of the effects of one treatment variable on an interval-scaled dependent variable.
A hypothesis-testing technique to determine whether statistically significant differences in means occur between two or more groups.
A method of comparing variances to make inferences about the means.
The substantive hypothesis tested is:
At least one group mean is not equal to another group mean.
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21. Partitioning Variance in ANOVA
Total Variability
Grand Mean
The mean of a variable over all observations.
SST = Total of (observed value-grand mean)2
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22. Partitioning Variance in ANOVA
Between-Groups Variance
The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations.
SSB = Total of ngroup(Group Mean − Grand Mean)2
Within-Group Error or Variance
The sum of the differences between observed values and the group mean for a given set of observations
Also known as total error variance.
SSE = Total of (Observed Mean − Group Mean)2
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23. The F-Test
F-Test
Used to determine whether there is more variability in the scores of one sample than in the scores of another sample.
Variance components are used to compute F-ratios
SSE, SSB, SST
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24. EXHIBIT 22.6 Interpreting ANOVA
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25. EXHIBIT 22.1–1 SPSS Output
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26. EXHIBIT 22A.1 A Test-Market Experiment on Pricing
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27. EXHIBIT 22A.2 ANOVA Summary Table
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28. EXHIBIT 22A.3 Pricing Experiment ANOVA Table
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29. EXHIBIT 22B.1 ANOVA Table for Randomized Block Designs
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30. EXHIBIT 22B.2 ANOVA Table for Two-Factor Design
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