17、ring 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 Comparing Proportions The hypothesis is: Ho: 1 2 may be restated as: Ho: 1 2 0 Copyright 2000 by H 。

18、arcourt, Inc. All rights reserved. A Z-Test for Differences of Proportions 21 : o H or 0: 21 o H Copyright 2000 by Harcourt, Inc. All rights reserved. Z-Test for Differences of Proportions 21 2121 pp S pp Z Copyright 2000 by Harcourt, Inc. All rights reserved. p1 = sample portion of successes in Gro 。

19、up 1 p2 = sample portion of successes in Group 2 1 1) = hypothesized population proportion 1 minus hypothesized population proportion 1 minus Sp1-p2 = pooled estimate of the standard errors of difference of proportions Z-Test for Differences of Proportions Copyright 2000 by Harcourt, Inc. All rights 。

20、 reserved. Z-Test for Differences of Proportions - to calculate the standard error of the difference of proportions 21 11 21 nn qpS pp Copyright 2000 by Harcourt, Inc. All rights reserved. p = pooled estimate of proportion of success in a sample of both groups p = (1- p) or a pooled estimate of prop 。

21、ortion of failures in a sample of both groups n1= sample size for group 1 n2= sample size for group 2 p qp Z-Test for Differences of Proportions - to calculate the standard error of the difference of proportions Copyright 2000 by Harcourt, Inc. All rights reserved. Z-Test for Differences of Proporti 。

22、ons - to calculate the standard error of the difference of proportions - weighted average 21 2211 nn pnpn p Copyright 2000 by Harcourt, Inc. All rights reserved. A Z-Test for Differences of Proportions 100 1 100 1 625.375. 21 pp S 068. Copyright 2000 by Harcourt, Inc. All rights reserved. 100100 4 . 。

23、10035.100 p 375. 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 Hypothesi 。

24、s when comparing three groups 1 2 3 Copyright 2000 by Harcourt, Inc. All rights reserved. groupswithinVariance groupsbetweenVariance F Analysis of Variance - F-Ratio Copyright 2000 by Harcourt, Inc. All rights reserved. Analysis of Variance - Sum of squares betweenwithintotal SS SS SS Copyright 2000 。

25、 by Harcourt, Inc. All rights reserved. Analysis of Variance - Sum of squares n i c j1 1 2 total )( SSXX ij 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 =。

26、number of all observations or test units in a group c = number of jth groups (or columns) ij X X Copyright 2000 by Harcourt, Inc. All rights reserved. n i c j j 1 1 2 within )( SSXX ij Analysis of Variance - Sum of squares Copyright 2000 by Harcourt, Inc. All rights reserved. Analysis of variance -。

27、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) ij X X Copyright 2000 by Harcourt, Inc. All rights reserved. n j jj n 1 2 between )( SSXX Analy 。

28、sis 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 observation or test unit in the jth group = grand mean nj = number of all observations or test units in a group j X X Copyright 2000 by Harc 。

29、ourt, Inc. All rights reserved. 1 c SS MS between between Analysis of Variance - Mean Squares Between Copyright 2000 by Harcourt, Inc. All rights reserved. ccn SS MS within within Analysis of Variance - Mean Square Within Copyright 2000 by Harcourt, Inc. All rights reserved. within between MS MS F A 。

30、nalysis 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 。

31、 99 X1=119.25 Test Market A, B, or C Test Market D, E, or F Test Market G, H, or I Test Market J, K, or L Mean Grand Mean Copyright 2000 by Harcourt, Inc. All rights reserved. ANOVA Summary Table Source of Variation Between Groups Sum of Squares SSBETWEEN Degrees of Freedom c-1 where c=number of gro 。

32、ups Mean Squared-MSBETWEEN SSBETWEEN/c-1 Copyright 2000 by Harcourt, Inc. All rights reserved. Within Groups Sum of Squares SSWITHIN Degrees of Freedom cn-c where c=number of groups, n= number of observations in a group Mean Squared-MSWITHIN SSWITHIN/cn-c ANOVA Summary Table Source of Variation Copy 。

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标题：BIVARIATE|BIVARIATE STATISTICS - TESTS OF DIFFERENCES( 二 )