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 D i = Y i − X i , i = 1, …, N the difference between two paired random variables. The classical Wilcoxon-signed-rank test assumes that the differences D i are mutually independent and D i , 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...
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References and Further Reading
Buck W (1979) Signed-rank tests in presence of ties (with extended tables). Biom J 21(6):501–526
Conover WJ (1973) On methods of handling ties in the Wilcoxon signed-rank test. J Am Stat Assoc 68(344):985–988
Higgins JJ (2004) An introduction to modern nonparametric statistics. Brooks/Cole, Pacific Grove
Hollander M, Wolfe DA (1999) Nonparametric statistical methods. 2nd edn. Wiley, New York
Pratt JW (1959) Remarks on zeros and ties in the Wilcoxon signed rank procedures. J Am Stat Assoc 54:655–667
Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1:80–83
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Rey, D., Neuhäuser, M. (2011). Wilcoxon-Signed-Rank Test. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_616
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