bivariate statistics-tests of differences.ppt

1、Exploring Marketing ResearchWilliam G. Zikmund,Chapter 22: Bivariate Statistics- Tests of Differences,天马行空官方博客： ；QQ:1318241189；QQ群：175569632,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:

2、 Permissions Department, Harcourt, Inc., 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

3、,Independent groups: t-test or Z-test,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 T

4、ests,Copyright 2000 by Harcourt, Inc. 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 rig

5、hts reserved.,Type of Measurement,Differences 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

6、Fit”,Copyright 2000 by Harcourt, Inc. 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

7、frequency 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,Cop

8、yright 2000 by Harcourt, Inc. All rights 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 Measureme

9、nt,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 scaled dependent variables t-test When groups are small When population standard deviation is unknown z-test W

10、hen groups are large,Copyright 2000 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,C

11、opyright 2000 by Harcourt, Inc. All 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 2

12、000 by Harcourt, Inc. All rights reserved.,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,Cop

13、yright 2000 by Harcourt, Inc. All rights 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

14、.,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,Copyright 2000 by Harcourt, Inc. All rights reserved.,Copyright 2000 by Harcourt, Inc. All rights reserved.,Type of Measurement,Diff

15、erences between two independent groups,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.,Dif

16、ferences Between Two Groups when Comparing 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 P

17、roportions,Copyright 2000 by Harcourt, Inc. All rights reserved.,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 1 minus Sp1-p2 = pooled estimate of the standard errors o

18、f difference of proportions,Z-Test for Differences of Proportions,Copyright 2000 by Harcourt, Inc. All rights reserved.,Z-Test for Differences of Proportions- to calculate the standard error of the difference of proportions,Copyright 2000 by Harcourt, Inc. All rights reserved.,p = pooled estimate of

19、 proportion of success in a sample of both groups p = (1- p) or a pooled estimate of proportion of failures in a sample of both groups n1= sample size for group 1 n2= sample size for group 2,Z-Test for Differences of Proportions- to calculate the standard error of the difference of proportions,Copyr

20、ight 2000 by Harcourt, Inc. All rights reserved.,Z-Test for Differences of Proportions- to calculate the standard error of the difference of proportions - weighted average,Copyright 2000 by Harcourt, Inc. All rights reserved.,A Z-Test for Differences of Proportions,Copyright 2000 by Harcourt, Inc. A

21、ll rights reserved.,A Z-Test for Differences of Proportions,Copyright 2000 by Harcourt, Inc. All rights reserved.,Type of Measurement,Differences between three or more independent groups,Interval or ratio,One-way ANOVA,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance,Hypoth

22、esis when comparing three groups m1 = m2 = m3,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - F-Ratio,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - Sum of squares,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance -

23、Sum of squares,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - Sum of squares,pi = individual scores, i.e., the ith observation or test unit in the jth group pi = grand mean n = number of all observations or test units in a group c = number of jth groups (or columns),Cop

24、yright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - Sum of squares,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of variance - Sum of squares,pi = individual scores, i.e., the ith observation or test unit in the jth group pi = grand mean n = number of all obser

25、vations or test units in a group c = number of jth groups (or columns),Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - Sum of squares,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - Sum of squares,= individual scores, i.e., the ith observatio

26、n or test unit in the jth group = grand mean nj = number of all observations or test units in a group,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - Mean Squares Between,Copyright 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - Mean Square Within,Copy

27、right 2000 by Harcourt, Inc. All rights reserved.,Analysis of Variance - Calculation of F-Ratio,Copyright 2000 by Harcourt, Inc. All rights reserved.,A Test Market Experiment on Pricing,Sales in Units (thousands),Regular Price $.99 130 118 87 84 X1=104.75 X=119.58,Reduced Price $.89 145 143 120 131 X2=134.75,Cents-Off Coupon Regular Price 153 129 96 99 X1=119.25,Test Market A, B, or C Test Market D, E,