MannWhitneyho

The Mann-Whitney U test, also known as the Wilcoxon rank-sum test, is a non-parametric statistical test used to compare two independent samples. It is employed when the assumptions of the independent samples t-test, such as the normality of the data, are not met. The Mann-Whitney U test assesses whether one of the two samples tends to have larger values than the other.

The null hypothesis for the Mann-Whitney U test states that the two samples are drawn from populations with identical distributions, or equivalently, that the probability of an observation from one sample being greater than an observation from the other sample is 0.5. The alternative hypothesis can be one-sided (e.g., one sample tends to have larger values) or two-sided (e.g., the samples come from populations with different distributions).

To perform the test, all observations from both samples are pooled and ranked in ascending order. Ranks are then summed separately for each sample. The U statistic is calculated based on these rank sums and the sample sizes. A smaller p-value indicates stronger evidence against the null hypothesis, suggesting a significant difference between the two samples. The Mann-Whitney U test is robust to outliers and suitable for ordinal data.