HW6 - Homework 6 Solutions 1. & 2. The...

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Unformatted text preview: Homework 6 Solutions 1. & 2. The permutation distribution of the slope, Spearmans r s and Kendalls 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 Spearmans rank correlation-1 -0.5 0.5 1 1 2 2 1-------------------------------------------------------------- Permutation distributions of the Kendalls tau-1 -0.33 0.33 1 1 2 2 1-------------------------------------------------------------- 4. Test for significant association Pearsons correlation H : = 0 H a : negationslash = 0 Spearmans rank correlation H : s = 0 H a : s negationslash = 0 Kendalls tau H : = 0 H a : negationslash = 0---------------------------------------------------------- Pearsons Correlation Test with t-distribution: Pearsons 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---------------------------------------------------------- Spearman Rank Correlation Test with normal distribution: Spearmans 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---------------------------------------------------------- Kendalls 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: Pearsons 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: Spearmans 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: Kendalls tau of original data: 0.3110463 estimated p-value for Kendalls tau= 0.2368 selected percentiles of Kendalls tau: 90% 95% 97.5% 99% 0.31 0.41 0.47 0.56----------------------------------------------------------...
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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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HW6 - Homework 6 Solutions 1. & 2. The...

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