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

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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 0 Self-administered 0 1 2 H 0 : 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
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---------------------------------------------------------- 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
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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 0 College B 2 2 3 2 1 College C 1 2 3 4 2 H 0 : 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
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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 Severe Moderate Slight None (1) (2) (3) (4) A 10 12 13 30 B 9 9 11 35 C 7 8 12 43 H 0 : τ A = τ B = τ C H a : τ A τ B τ C ---------------------------------------------------------- Pearsons’ Chi-square Test with approximation: Pearson’s Chi-squared test data: trt.mat X-squared = 4.9649, df = 6, p-value = 0.5483 ---------------------------------------------------------- ---------------------------------------------------------- Kruskal-Wallis Test with approximation: Kruskal-Wallis rank sum test data: Insect by Insect.ind Kruskal-Wallis chi-squared = 3.9586, df = 2, p-value = 0.1382 ---------------------------------------------------------- -------------------------------------------------------- Jonckheere-Terpstra Permutation Test -------------------------------------------------------- Number of Permutation: 5000 JT_obs: 5253 p-value= 0.026 -------------------------------------------------------- 4
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Odds Ratio
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