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1、Exploring Marketing Research William G. Zikmund,Chapter 22: Bivariate Statistics- Tests of Differences,Copyright 2000 by Harcourt, Inc. All rights reserved. Requests for permission to make copies of any part of the work should be mailed to the following address: Permissions Department, Harcourt, Inc
2、., 6277 Sea Harbor Drive, Orlando Florida 32887-6777,Copyright 2000 by Harcourt, Inc. All rights reserved.,Common Bivariate Tests,Type of Measurement,Differences between two independent groups,Differences among three or more independent groups,Interval and ratio,Independent groups: t-test or Z-test,
3、One-way ANOVA,Copyright 2000 by Harcourt, Inc. All rights reserved.,Type of Measurement,Differences between two independent groups,Differences among three or more independent groups,Ordinal,Mann-Whitney U-test Wilcoxon test,Kruskal-Wallis test,Common Bivariate Tests,Copyright 2000 by Harcourt, Inc.
4、All rights reserved.,Type of Measurement,Differences between two independent groups,Differences among three or more independent groups,Nominal,Z-test (two proportions) Chi-square test,Chi-square tst,Common Bivariate Tests,Copyright 2000 by Harcourt, Inc. All rights reserved.,Type of Measurement,Diff
5、erences between two independent groups,Nominal,Chi-square test,Copyright 2000 by Harcourt, Inc. All rights reserved.,Differences Between Groups,Contingency Tables Cross-Tabulation Chi-Square allows testing for significant differences between groups “Goodness of Fit”,Copyright 2000 by Harcourt, Inc.
6、All rights reserved.,Chi-Square Test,x = chi-square statistics Oi = observed frequency in the ith cell Ei = expected frequency on the ith cell,Copyright 2000 by Harcourt, Inc. All rights reserved.,Ri = total observed frequency in the ith row Cj = total observed frequency in the jth column n = sample
7、 size,Chi-Square Test,D.f.=(R-1)(C-1),Copyright 2000 by Harcourt, Inc. All rights reserved.,Degrees of Freedom,Copyright 2000 by Harcourt, Inc. All rights reserved.,Awareness of Tire Manufacturers Brand Men Women Total,Aware 50 10 60 Unaware 15 25 40 65 35 100,Copyright 2000 by Harcourt, Inc. All ri
8、ghts reserved.,Chi-Square Test: Differences Among Groups Example,Copyright 2000 by Harcourt, Inc. All rights reserved.,Copyright 2000 by Harcourt, Inc. All rights reserved.,X2=3.84 with 1 d.f.,Copyright 2000 by Harcourt, Inc. All rights reserved.,Type of Measurement,Differences between two independe
9、nt groups,Interval and ratio,t-test or Z-test,Copyright 2000 by Harcourt, Inc. All rights reserved.,Differences Between Groups when Comparing Means,Ratio scaled dependent variables t-test When groups are small When population standard deviation is unknown z-test When groups are large,Copyright 2000
10、by Harcourt, Inc. All rights reserved.,Null Hypothesis About Mean Differences Between Groups,Copyright 2000 by Harcourt, Inc. All rights reserved.,t-Test for Difference of Means,Copyright 2000 by Harcourt, Inc. All rights reserved.,t-Test for Difference of Means,Copyright 2000 by Harcourt, Inc. All
11、rights reserved.,t-Test for Difference of Means,Copyright 2000 by Harcourt, Inc. All rights reserved.,X1 = mean for Group 1 X2 = mean for Group 2 SX1-X2 = the pooled or combined standard error of difference between means.,t-Test for Difference of Means,Copyright 2000 by Harcourt, Inc. All rights res
12、erved.,Pooled estimate of the standard error,Copyright 2000 by Harcourt, Inc. All rights reserved.,S12 = the variance of Group 1 S22 = the variance of Group 2 n1 = the sample size of Group 1 n2 = the sample size of Group 2,Pooled estimate of the standard error,Copyright 2000 by Harcourt, Inc. All ri
13、ghts reserved.,Pooled estimate of the Standard Error t-Test for the difference of Means,S12 = the variance of Group 1 S22 = the variance of Group 2 n1 = the sample size of Group 1 n2 = the sample size of Group 2,Copyright 2000 by Harcourt, Inc. All rights reserved.,Degrees of Freedom,d.f. = n - k wh
14、ere: n = n1 + n2 k = number of groups,Copyright 2000 by Harcourt, Inc. All rights reserved.,t-Test for Difference of Means -example,Copyright 2000 by Harcourt, Inc. All rights reserved.,Copyright 2000 by Harcourt, Inc. All rights reserved.,Type of Measurement,Differences between two independent grou
15、ps,Nominal,Z-test (two proportions),Copyright 2000 by Harcourt, Inc. All rights reserved.,Comparing Two Groups when Comparing Proportions,Percentage Comparisons Sample Proportion - P Population Proportion -,Copyright 2000 by Harcourt, Inc. All rights reserved.,Differences Between Two Groups when Com
16、paring Proportions,The hypothesis is: Ho: P1 = P2 may be restated as: Ho: P1 - P2 = 0,Copyright 2000 by Harcourt, Inc. All rights reserved.,A Z-Test for Differences of Proportions,or,Copyright 2000 by Harcourt, Inc. All rights reserved.,Z-Test for Differences of Proportions,Copyright 2000 by Harcourt, Inc. All rights reserved.,p1 = sample portion of successes in Group 1 p2 = sample
