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Mann–Whitney test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.
The test is named after Frank Wilcoxon (1892–1965) who, in a single paper, proposed both it and the rank-sum test for two independent samples. [3] The test was popularized by Sidney Siegel (1956) in his influential textbook on non-parametric statistics. [4]
The Kruskal–Wallis test' by ranks, Kruskal–Wallis test (named after William Kruskal and W. Allen Wallis), or one-way ANOVA on ranks is a non-parametric statistical test for testing whether samples originate from the same distribution. [ 1 ][ 2 ][ 3 ] It is used for comparing two or more independent samples of equal or different sample sizes.
To test the difference between groups for significance a Wilcoxon rank sum test is used, which also justifies the notation W A and W B in calculating the rank sums. From the rank sums the U statistics are calculated by subtracting off the minimum possible score, n(n + 1)/2 for each group: [1] U A = 54 − 7(8)/2 = 26 U B = 37 − 6(7)/2 = 16
Over his career Wilcoxon published over 70 papers. [3] His most well-known paper [4] contained the two new statistical tests that still bear his name, the Wilcoxon rank-sum test and the Wilcoxon signed-rank test. These are non-parametric alternatives to the unpaired and paired Student's t-tests respectively. He died on November 18, 1965.
The sign test is a statistical test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment. Given pairs of observations (such as weight pre- and post-treatment) for each subject, the sign test determines if one member of the pair (such as pre-treatment) tends to be greater than (or less than) the other member of the pair (such as ...
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A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them. For example, two common nonparametric methods of significance that use rank correlation are the Mann–Whitney U test and the Wilcoxon signed-rank test.