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# HW3 - Homework 3 Solutions 1 3 K-sample Permutation F-test...

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Homework 3 Solutions 1. & 3. K -sample Permutation F -test and one-way ANOVA/ Kruskal-Wallis test H 0 : τ 1 = τ 2 = τ 3 H a : at least one of τ i negationslash = τ j _______________________________________________________ ANOVA Table: DF SS MS F p-value Treatment 2 7.14 3.57 2.99 0.088 Error 12 14.32 1.19 NA NA Total 14 21.45 NA NA NA _______________________________________________________ -------------------------------------------------------- Permutation Test -------------------------------------------------------- F_obs: 2.99 SSX_obs: 39.52 Number of Permutation: 5000 p-value based on SSX 0.07 p-value based on F 0.07 -------------------------------------------------------- -------------------------------------------------------- Kruskal-Wallis rank sum test data: G by G.inK Kruskal-Wallis chi-squared = 5.78, df = 2, p-value = 0.05558 -------------------------------------------------------- -------------------------------------------------------- Permutation Test of Kruskall-Wallis -------------------------------------------------------- KW_obs: 5.78 Number of Permutation: 10000 p-value based on SSX 0.05 -------------------------------------------------------- We fail to reject H 0 for all three tests at significance level α = 0 . 05, but we reject H 0 at α = 0 . 10. However, from the permutation test of Kruskall-Wallis, we observe that the estimated exact p value is 0 . 05. Thus, we reject H 0 at significant level α = 0 . 05. From the boxplots, we find out outliers in Group 1 and Group 3. It might be the reason why we got smaller p value in Kruskal- Wallis test. Also, it might be the reason why p value of the permutation F -test is similar to that of ANOVA.

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