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Although Henry Mann and Donald Ransom Whitney [1] developed the Mann–Whitney U test under the assumption of continuous responses with the alternative hypothesis being that one distribution is stochastically greater than the other, there are many other ways to formulate the null and alternative hypotheses such that the Mann–Whitney U test will give a valid test.
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Mann–Whitney U or Wilcoxon rank sum test: tests whether two samples are drawn from the same distribution, as compared to a given alternative hypothesis. McNemar's test : tests whether, in 2 × 2 contingency tables with a dichotomous trait and matched pairs of subjects, row and column marginal frequencies are equal.
The Wilcoxon–Mann–Whitney U two-sample test or its generalisation for more samples, the Kruskal–Wallis test, can often be considered instead. The relevant aspect of the median test is that it only considers the position of each observation relative to the overall median, whereas the Wilcoxon–Mann–Whitney test takes the ranks of each ...
Statistical tests are used to test the fit between a hypothesis and the data. [1] [2] Choosing the right statistical test is not a trivial task. [1]The choice of the test depends on many properties of the research question.
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A normal quantile plot for a simulated set of test statistics that have been standardized to be Z-scores under the null hypothesis. The departure of the upper tail of the distribution from the expected trend along the diagonal is due to the presence of substantially more large test statistic values than would be expected if all null hypotheses were true.
Z-test – Statistical test; Mann–Whitney U test – Nonparametric test of the null hypothesis; Šidák correction for t-test – Statistical method; Welch's t-test – Statistical test of whether two populations have equal means; Analysis of variance – Collection of statistical models (ANOVA) t-distribution – Probability distribution