Mann–Whitney U Test
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Mann–Whitney U Test
The Mann–Whitney U 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 randomly selected values ''X'' and ''Y'' from two populations have the same distribution. Nonparametric tests used on two ''dependent'' samples are the sign test and the Wilcoxon signed-rank test. Assumptions and formal statement of hypotheses Although Henry Mann and Donald Ransom Whitney 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. A very general formulation is to assume that: # All the observations from both groups are independent of each other, # The responses are at least ordinal (i.e., one ...
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Wilcoxon Signed-rank Test
The Wilcoxon signed-rank test is a non-parametric rank test for statistical hypothesis testing used either to test the location of a population based on a sample of data, or to compare the locations of two populations using two matched samples., p. 350 The one-sample version serves a purpose similar to that of the one-sample Student's ''t''-test. For two matched samples, it is a paired difference test like the paired Student's ''t''-test (also known as the "''t''-test for matched pairs" or "''t''-test for dependent samples"). The Wilcoxon test is a good alternative to the t-test when the normal distribution of the differences between paired individuals cannot be assumed. Instead, it assumes a weaker hypothesis that the distribution of this difference is symmetric around a central value and it aims to test whether this center value differs significantly from zero. The Wilcoxon test is a more powerful alternative to the sign test because it considers the magnitude of the differ ...
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