note15 - Chapter 5: Tests for Trends and Association 6....

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Unformatted text preview: Chapter 5: Tests for Trends and Association 6. Contingency Tables with Ordered Categories • alternatives to the χ 2 statistic when there is an ordering among the cate- gories of one or both factors in a contingency table • Singly Ordered Tables – the categories of one of the factors is ordered – numerical labels with increasing ordering – Wilcoxon rank-sum test with ties when the unordered factor has two categories Not Somewhat Very satisfied satisfied satisfied Physician-prescribed 2 2 Self-administered 1 2 H : no difference between the two methods of pain relief H a : the self-administered dose will be more satisfactory Level of Satisfaction with Pain Relief Physician-prescribed 1,1,2,2 Self-administered 2,3,3---------------------------------------------------------- Permutation Chi-square test: Number of the random permutations: R= 5000 Chi-square of original data: chi-square= 4.277778 estimated p-value for Chi-square test= 0.3132---------------------------------------------------------- 1---------------------------------------------------------- Mann-Whitney-Wilcoxon test: Exact Wilcoxon rank sum test data: pp and sa W = 1, p-value = 0.08571 alternative hypothesis: true mu is less than 0-------------------------------------------------------------------------------------------------------------------- Permutation Test with Rank Sum Rank sum for trt: 11 p-value: 0.08571429------------------------------------------------------------------------------------------------------------------ Jonckheere-Terpstra Permutation Test-------------------------------------------------------- Number of all possible permutations: 35 JT_obs: 10 p-value= 0.086-------------------------------------------------------- 2 – Kruskal-Wallis test with ties when the unordered factor has more than two categories ∗ Ratings of the chief Academic Officer at Hypothetical State Uni- versity Poor Fair Good Very Good Excellent (1) (2) (3) (4) (5) College A 6 4 3 2 College B 2 2 3 2 1 College C 1 2 3 4 2 H : The ratings of the chief academic officer of College A, B and C are the same---------------------------------------------------------- Pearsons’ Chi-square Test with approximation: Pearson’s Chi-squared test data: data.mat X-squared = 7.0231, df = 8, p-value = 0.5341 Warning message: In chisq.test(data.mat) : Chi-squared approximation may be incorrect---------------------------------------------------------- College A 1,1,1,1,1,1,2,2,2,2,3,3,3,4,4 College B 1,1,2,2,3,3,3,4,4,5 College C 1,2,2,3,3,3,4,4,4,4,5,5---------------------------------------------------------- Kruskal-Wallis Test with approximation: Kruskal-Wallis rank sum test data: College by College.ind Kruskal-Wallis chi-squared = 6.4283, df = 2, p-value = 0.04019---------------------------------------------------------- 3 • Double Ordered Tables – the categories of both factors are ordered – Jonckheere-Terpstra with ties ∗ Level of Insect Damage for Each of Three Treatments Response/Treatment...
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This note was uploaded on 07/22/2011 for the course STA 4502 taught by Professor Staff during the Spring '08 term at University of Florida.

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note15 - Chapter 5: Tests for Trends and Association 6....

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