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The 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.
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It extends the Mann–Whitney U test, which is used for comparing only two groups. The parametric equivalent of the Kruskal–Wallis test is the one-way analysis of variance (ANOVA). A significant Kruskal–Wallis test indicates that at least one sample stochastically dominates one other sample. The test does not identify where this stochastic ...
It is thus highly similar to the well-known Mann–Whitney U test. The core difference is that the Mann-Whitney U test assumes equal variances and a location shift model, while the Brunner Munzel test does not require these assumptions, making it more robust and applicable to a wider range of conditions. As a result, multiple authors recommend ...
Median test (also Mood’s median-test, Westenberg-Mood median test or Brown-Mood median test) is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two or more samples are drawn are identical. The data in each sample are assigned to two groups ...
Henry Berthold Mann (27 October 1905, Vienna – 1 February 2000, Tucson) [1] was a professor of mathematics and statistics at the Ohio State University. Mann proved the Schnirelmann-Landau conjecture in number theory, and as a result earned the 1946 Cole Prize. He and his student developed the ("Mann-Whitney") U-statistic of nonparametric ...
One would not accept the null hypothesis, concluding that there is strong evidence that the expected values in the three groups differ. The p-value for this test is 0.002. After performing the F-test, it is common to carry out some "post-hoc" analysis of the group means. In this case, the first two group means differ by 4 units, the first and ...
Jarque–Bera test, Anderson–Darling test, Cramér–von Mises criterion, Kolmogorov–Smirnov test: this test only works if the mean and the variance of the normal distribution are assumed known under the null hypothesis, Lilliefors test: based on the Kolmogorov–Smirnov test, adjusted for when also estimating the mean and variance from the ...