Tests for Ranked Data

"Ranking" refers to the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.

The Mann–Whitney $U$-test is a non-parametric test of the null hypothesis that two populations are the same against an alternative hypothesis.

The Wilcoxon $t$-test assesses whether population mean ranks differ for two related samples, matched samples, or repeated measurements on a single sample.

The Kruskal–Wallis one-way analysis of variance by ranks is a non-parametric method for testing whether samples originate from the same distribution.