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HW5 - Homework 5 Solutions 1 3 The permutation distribution...

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Homework 5 Solutions 1. & 3. The permutation distribution of the mean of the differences and of the signed- rank statistic -------------------------------------------------------------- Number of All Possible Permuations: 16 -------------------------------------------------------------- Permutation distributions of the mean of the differences d.bar -8 -7 -4 -3 -2 -1 0.0625 0.0625 0.0625 0.1250 0.1250 0.0625 d.bar 1 2 3 4 7 8 0.0625 0.1250 0.1250 0.0625 0.0625 0.0625 -------------------------------------------------------------- Permutation distributions of the signed-rank statistic s.plus 0 2 8 10 12 14 0.0625 0.0625 0.0625 0.1250 0.1250 0.0625 s.plus 18 20 22 24 30 32 0.0625 0.1250 0.1250 0.0625 0.0625 0.0625 -------------------------------------------------------------- SR + = 2 × D + 16 1

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2. & 5. A paired-comparison permutation test and the Wilcoxon signed-rank test H 0 : F ( x ) = 1 F ( x ) H a : F ( x ) negationslash = 1 F ( x ) There are ties (difference = 0) in data set. A permutation test and the Wilcoxon signed-rank test has been done with zeros. -------------------------------------------------------------- Paired-comparison permutation test Number of All Possible Permuations: 524288 number of permutations: R= 5000 D.bar_obs= -0.58 two-sided p-value=1/R sum{I(abs(D.bar_b) > abs(D.bar_obs))}= 0.037 S.plus_obs= 2 two-sided p-value=2*1/R sum{I(S.plus_b < S.plus_obs)}= 0.033 -------------------------------------------------------------- -------------------------------------------------------------- Exact Wilcoxon signed rank test data: Before and After V = 9, p-value = 0.9956 alternative hypothesis: true mu is greater than 0
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