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Wilcoxon signed-rank test

The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test (also known as 't-test for matched pairs' or 't-test for dependent samples') when the population cannot be assumed to be normally distributed. A Wilcoxon signed-rank test is a nonparametric test that can be used to determine whether two dependent samples were selected from populations having the same distribution. The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test (also known as 't-test for matched pairs' or 't-test for dependent samples') when the population cannot be assumed to be normally distributed. A Wilcoxon signed-rank test is a nonparametric test that can be used to determine whether two dependent samples were selected from populations having the same distribution. The test is named for Frank Wilcoxon (1892–1965) who, in a single paper, proposed both it and the rank-sum test for two independent samples (Wilcoxon, 1945). The test was popularized by Sidney Siegel (1956) in his influential textbook on non-parametric statistics. Siegel used the symbol T for a value related to, but not the same as, W {displaystyle W} . In consequence, the test is sometimes referred to as the Wilcoxon T test, and the test statistic is reported as a value of T. Let N {displaystyle N} be the sample size, i.e., the number of pairs. Thus, there are a total of 2N data points. For pairs i = 1 , . . . , N {displaystyle i=1,...,N} , let x 1 , i {displaystyle x_{1,i}} and x 2 , i {displaystyle x_{2,i}} denote the measurements. In historical sources a different statistic, denoted by Siegel as the T statistic, was used. The T statistic is the smaller of the two sums of ranks of given sign; in the example, therefore, T would equal 3+4+5+6=18. Low values of T are required for significance. T is easier to calculate by hand than W and the test is equivalent to the two-sided test described above; however, the distribution of the statistic under H 0 {displaystyle H_{0}} has to be adjusted. Note: Critical T values ( T c r i t {displaystyle T_{crit}} ) by values of N r {displaystyle N_{r}} can be found in appendices of statistics textbooks, for example in Table B-3 of Nonparametric Statistics: A Step-by-Step Approach, 2nd Edition by Dale I. Foreman and Gregory W. Corder(https://www.oreilly.com/library/view/nonparametric-statistics-a/9781118840429/bapp02.xhtml). As demonstrated in the example, when the difference between the groups is zero, the observations are discarded. This is of particular concern if the samples are taken from a discrete distribution. In these scenarios the modification to the Wilcoxon test by Pratt 1959, provides an alternative which incorporates the zero differences. This modification is more robust for data on an ordinal scale. To compute an effect size for the signed-rank test, one can use the rank-biserial correlation.

[ "Statistics", "Surgery", "test", "Rank-Sum Tests", "Sign test", "Paired difference test", "wilcoxon norm", "Van der Waerden test" ]
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