MannWhitneyn

MannWhitneyn refers to the Mann-Whitney U test, a nonparametric statistical method used to compare two independent samples. It is also known as the Mann-Whitney-Wilcoxon test or the Wilcoxon rank-sum test. The test was developed by Henry Mann and Donald Whitney in 1947, and it is commonly described alongside the Wilcoxon rank-sum approach in statistical literature.

The Mann-Whitney U test is appropriate when the data are ordinal or not normally distributed, and when the two samples are independent. It does not require the assumption of normality and is often used as an alternative to the two-sample t-test when its assumptions are in doubt. The test assesses whether one population tends to yield larger values than the other, effectively comparing distributions rather than means per se. If the two distributions have the same shape, the test can be interpreted as a test of medians; otherwise it reflects differences in the overall distribution.

Methodologically, the observations from both groups are pooled and ranked. The sum of ranks for one group is used to compute the U statistic, which can be converted to a Z score for larger samples. There are two U values, and the smaller one is typically used to determine the p-value. Tied observations are adjusted in the calculation. In large samples, a normal approximation is commonly employed, while exact methods exist for small samples.

Limitations include reduced power relative to parametric tests when those tests’ assumptions hold, and sensitivity to differences in distribution shapes beyond central tendency. Effect sizes can be reported using rank-based measures such as r.