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# slide18 - Wilcoxon Signed-Rank Test Uses both...

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1 ± Uses both direction (sign) and magnitude. ± Applies to the case of symmetric continuous distributions: ± Mean equals median. Wilcoxon Signed-Rank Test 2 ± H 0 : µ = µ 0 ± Compute differences, X i µ 0 , i = 1,2,…,n ± Rank the absolute differences | X i µ 0 | ± W + = sum of positive ranks ± W = sum of negative ranks ± From Table X in Appendix: critical w α * ± What are the rejection criteria for different H 1 ? Method

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3 ± If sample size is large, n > 20 ± W + (or W ) is approximately normal with Large Samples 2 (1 ) 4 ) ( 21 ) 24 W W nn n µ σ + + + = ++ = 4 ± Paired data has to be from two continuous distributions that differ only wrt their means. ± Their distributions need not be symmetric. ± This ensures that the distribution of the differences is continuous and symmetric. Paired Observations
5 ± If underlying population is normal, t-test is best (has lowest β ). ± The Wilcoxon signed-rank test will never be much worse than the t-test, and in many nonnormal cases it may be superior. ± The Wilcoxon signed-ran test is a useful alternate to the t-test.

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slide18 - Wilcoxon Signed-Rank Test Uses both...

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