Robust Kruskal-Wallis test

The robust Kruskal-Wallis test is a nonparametric, rank-based method for comparing three or more independent groups when data contain outliers, heavy tails, or heterogeneous spread. It augments the classical Kruskal-Wallis H statistic with robust techniques — such as trimmed means on ranks or permutation-based inference — to maintain valid Type I error rates even when distributional assumptions are violated.