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wilcoxon-signed-ranks

# wilcoxon-signed-ranks - The Wilcoxon Signed Ranks Test...

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The Wilcoxon Signed Ranks Test Douglas Whitaker February 25, 2012 These notes should help clarify how the Wilcoxon Signed Ranks Test works for all three possible alter- native hypotheses. 1 Assumptions The Wilcoxon Signed Ranks Test is the nonparametric alternative to the matched-pairs t-test, meaning that if the assumptions for the matched-pairs t-test are violated, this should be the next method we look at. Its assumptions are: Data obtained from randomization Data are matched pairs Quantitative response Note the lack of a sample size or normality assumption (this lack is what makes it ‘nonparametric’). 2 Hypotheses Our null hypothesis for this test is H 0 : the median of the differences = 0 There are three possible alternative hypotheses, and the one you choose will be based on the research question we’re trying to answer. I’ll give examples of all three below. H A : the median of the differences > 0 H A : the median of the differences < 0 H A : the median of the differences 6 = 0 Remember, we’re using the median rather than the mean because we will rank the data. It isn’t appropriate to use the mean with ranked data. 3 The Problem (This problem is from A&F Chapter 15.) A diet (one where participants aren’t allowed drinks containing high fructose corn syrup) claims to promote weight loss. To that end, a pilot study is performed with three participants. The data collected are: 1

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Subject Pre-Diet Post-Diet Difference 1 172 160 12 2 210 195 15 3 168 170 -2
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wilcoxon-signed-ranks - The Wilcoxon Signed Ranks Test...

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