Mann‐Whitney U Test

Abstract

The Mann‐Whitney U test, which is also known as the Wilcoxon rank sum test, tests for differences between two groups on a single, ordinal variable with no specific distribution (Mann & Whitney, 1947; Wilcoxon, 1945). In contrast, the independent samples t‐test, which is also a test of two groups, requires the single variable to be measured at the interval or ratio level, rather than the ordinal level, and to be normally distributed. We accordingly refer to the Mann‐Whitney U test as the nonparametric version of the parametric t‐test. Both tests require two independently sampled groups and assess whether two groups differ on a single, continuous variable. The two tests, however, differ on the assumed distribution. A nonparametric test assumes no specific distribution, whereas a parametric test assumes a specific distribution. Thus, the Mann‐Whitney U is conceptually similar to the t‐test for determining whether two sampled groups are from a single population. When data do not meet the parametric assumptions of the t‐test, the Mann‐Whitney U tends to be more appropriate.