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# HW6 - Homework 6 Solutions 1 2 The permutation distribution...

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Homework 6 Solutions 1. & 2. The permutation distribution of the slope, Spearman’s r s and Kendall’s τ for the height and weight -------------------------------------------------------------- Number of All Possible Permuations: 6 -------------------------------------------------------------- Permutation distribution of the slope of the least squares line -2.5 -1.96 -0.36 1.25 2.32 1 1 1 2 1 -------------------------------------------------------------- Permutation distributions of the Spearman’s rank correlation -1 -0.5 0.5 1 1 2 2 1 -------------------------------------------------------------- Permutation distributions of the Kendall’s tau -1 -0.33 0.33 1 1 2 2 1 -------------------------------------------------------------- 4. Test for significant association Pearson’s correlation H 0 : ρ = 0 H a : ρ negationslash = 0 Spearman’s rank correlation H 0 : ρ s = 0 H a : ρ s negationslash = 0 Kendall’s tau H 0 : τ = 0 H a : τ negationslash = 0 ---------------------------------------------------------- Pearsons’ Correlation Test with t-distribution: Pearson’s product-moment correlation data: mother and daughter t = 1.541, df = 9, p-value = 0.1577 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.1969458 0.8294436 sample estimates: cor 0.4569098 1

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---------------------------------------------------------- Spearman Rank Correlation Test with normal distribution: Spearman’s rank correlation rho data: mother and daughter S = 125.7779, p-value = 0.1915 alternative hypothesis: true rho is not equal to 0 sample estimates: rho 0.4282821 ---------------------------------------------------------- Kendall’s rank correlation tau data: mother and daughter z = 1.2751, p-value = 0.2023 alternative hypothesis: true tau is not equal to 0 sample estimates: tau 0.3110463 Warning message: In cor.test.default(mother, daughter, method = "kendall") : Cannot compute exact p-value with ties ---------------------------------------------------------- Permutation tests ---------------------------------------------------------- Number of the random permutations: R= 10000 ---------------------------------------------------------- Testing H0:rho=0 vs. Ha:rho=/=0: Pearson’s correlation of original data: 0.4569098 estimated p-value for Pearson correlation= 0.16 selected percentiles of Pearson correlations: 90% 95% 97.5% 99% 0.42 0.52 0.60 0.69 ---------------------------------------------------------- Testing H0:rho_s=0 vs. Ha:rho_s=/=0: Spearman’s correlation of original data: 0.4282821 estimated p-value for Spearman correlation= 0.189 2
selected percentiles of Spearman correlations: 90% 95% 97.5% 99% 0.42 0.53 0.62 0.70 ---------------------------------------------------------- Testing H0:tau=0 vs. Ha:tau=/=0: Kendall’s tau of original data: 0.3110463 estimated p-value for Kendall’s tau= 0.2368 selected percentiles of Kendall’s tau: 90% 95% 97.5% 99% 0.31 0.41 0.47 0.56 ---------------------------------------------------------- From all tests, we fail to reject H 0 even at significant level α = 0 . 1 5. Test for significant association with ties H 0 : τ = 0 H a : τ negationslash = 0 --------------------------------------------------------- Spearman Rank Correlation Test with normal distribution:

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HW6 - Homework 6 Solutions 1 2 The permutation distribution...

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