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

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 © 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.

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. © 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.

EXHIBIT 22.1 Some Bivariate Hypotheses © 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.

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. © 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.

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 © 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.

Degrees of Freedom (d.f.) d.f.=(R-1)(C-1) © 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.

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. © 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.

Example: Papa John’s Restaurants (cont’d) In this example, χ2 = 22.16 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? © 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.

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. © 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.

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. © 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.

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. © 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.

EXHIBIT 22.2 Independent Samples t-Test Results © 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.

EXHIBIT 22.3 SAS t-Test Output © 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.

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. © 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.

EXHIBIT 22.4 Example Results for a Paired Samples t-Test © 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.

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 © 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.

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 © 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.

The Z-Test for Comparing Two Proportions To calculate the standard error of the differences in proportions: © 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.

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. © 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.

Partitioning Variance in ANOVA Total Variability Grand Mean The mean of a variable over all observations. SST = Total of (observed value-grand mean)2 © 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.

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 © 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.

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 © 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.

EXHIBIT 22.6 Interpreting ANOVA © 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.

EXHIBIT 22.1–1 SPSS Output © 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.

EXHIBIT 22A.1 A Test-Market Experiment on Pricing © 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.

EXHIBIT 22A.2 ANOVA Summary Table © 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.

EXHIBIT 22A.3 Pricing Experiment ANOVA Table © 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.

EXHIBIT 22B.1 ANOVA Table for Randomized Block Designs © 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.

EXHIBIT 22B.2 ANOVA Table for Two-Factor Design © 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.