Wilcoxon-Signed-Rank Test

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The Wilcoxon-signed-rank test was proposed together with the Wilcoxon-rank-sum test (see WilcoxonMann Whitney Test) in the same paper by Frank Wilcoxon in 1945 (Wilcoxon 1945) and is a nonparametric test for the one-sample location problem. The test is usually applied to the comparison of locations of two dependent samples. Other applications are also possible, e.g., to test the hypothesis that the median of a symmetrical distribution equals a given constant. As with many nonparametric tests, the distribution-free test is based on ranks.

To introduce the classical Wilcoxon-signed-rank test and also important further developments of it we denote by Di = Yi − Xi, i = 1, , N the difference between two paired random variables. The classical Wilcoxon-signed-rank test assumes that the differences Di are mutually independent and Di, i = 1, , N comes from a continuous distribution F that is symmetric about a median θ. The continuity assumption on the distribution of the differences implies th ...