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Unformatted text preview: 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 matchedpairs ttest, meaning that if the assumptions for the matchedpairs ttest 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 : the median of the differences = 0 There are three possible alternative hypotheses, and the one you choose will be based on the research question were trying to answer. Ill give examples of all three below. H A : the median of the differences > H A : the median of the differences < H A : the median of the differences 6 = 0 Remember, were using the median rather than the mean because we will rank the data. It isnt appropriate to use the mean with ranked data. 3 The Problem (This problem is from A&F Chapter 15.) A diet (one where participants arent 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 Subject PreDiet PostDiet Difference 1 172 160 12 2 210 195 15 3 168 1702 In this study, a weight...
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This note was uploaded on 03/20/2012 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.
 Spring '08
 TA

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