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.。

【BIVARIATE|BIVARIATE STATISTICS - TESTS OF DIFFERENCES】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 i ii )( E EO x 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. n CR E ji ij Ri = total observed frequency in the ith row Cj = total observed frequency。

7、in the jth column n = sample 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 MenWomenTotal Aware 50 10 60 Unaware 15 25 40 65 35 100 Copyright 200 。

8、0 by Harcourt, Inc. All rights reserved. Chi-Square Test: Differences Among Groups Example 21 )2110( 39 )3950( 22 2 X 14 )1425( 26 )2615( 22 Copyright 2000 by Harcourt, Inc. All rights reserved. 161.22 643. 8654. 4762. 5102. 3 2 2 Copyright 2000 by Harcourt, Inc. All rights reserved. 1) 12)(12(. ) 1 。

9、)(1(. fd CRfd X2=3.84 with 1 d.f. Copyright 2000 by Harcourt, Inc. All rights reserved. Type of Measurement Differences between two independent groups Interval and ratio t-test or Z-test Copyright 2000 by Harcourt, Inc. All rights reserved. Differences Between Groups when Comparing Means Ratio scale 。

10、d dependent variables t-test When groups are small When population standard deviation is unknown z-test When groups are large Copyright 2000 by Harcourt, Inc. All rights reserved. Null Hypothesis About Mean Differences Between Groups 0 21 21 OR Copyright 2000 by Harcourt, Inc. All rights reserved. t 。

11、-Test for Difference of Means meansrandomofyVariabilit MeanMean t 21 Copyright 2000 by Harcourt, Inc. All rights reserved. 21 21 XX S t 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 200 。

12、0 by Harcourt, Inc. All rights reserved. 21 21 XX S t 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。

13、2000 by Harcourt, Inc. All rights reserved. Pooled estimate of the standard error 2121 2 22 2 11 11 2 ) 1(1 21 nnnn SnSn S XX 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 Grou 。

14、p 2 Pooled estimate of the standard error Copyright 2000 by Harcourt, Inc. All rights reserved. Pooled estimate of the Standard Error t-Test for the difference of Means 2121 2 22 2 11 11 2 ) 1(1 21 nnnn SnSn S XX S12 = the variance of Group 1 S22 = the variance of Group 2 n1 = the sample size of Gro 。

15、up 1 n2 = the sample size of Group 2 Copyright 2000 by Harcourt, Inc. All rights reserved. Degrees of Freedom d.f. = n - k where: n = n1 + n2 k = number of groups Copyright 2000 by Harcourt, Inc. All rights reserved. t-Test for Difference of Means -example 14 1 21 1 33 6 . 2131 . 220 22 21 XX S 797. 。

16、 Copyright 2000 by Harcourt, Inc. All rights reserved. 797. 2 .125 .16 t 797. 3 . 4 395. 5 Copyright 2000 by Harcourt, Inc. All rights reserved. Type of Measurement Differences between two independent groups Nominal Z-test (two proportions) Copyright 2000 by Harcourt, Inc. All rights reserved. Compa 。

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标题：BIVARIATE|BIVARIATE STATISTICS - TESTS OF DIFFERENCES