مقایسهٔ روش‌ها

	آزمون برونر-مونزل	آزمون H کروسکال-والیس
حوزه	آمار	آمار
خانواده	Hypothesis test	Hypothesis test
سال پیدایش	2000	1952
پدیدآور	Edgar Brunner & Ullrich Munzel	William Kruskal & W. Allen Wallis
نوع	Nonparametric two-sample comparison	Nonparametric group comparison
منبع بنیادین	Brunner, E. & Munzel, U. (2000). The Nonparametric Behrens-Fisher Problem: Asymptotic Theory and a Small-Sample Approximation. Biometrical Journal, 42(1), 17–25.	Kruskal, W. H. & Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583–621.
نام‌های دیگر	Brunner-Munzel Testi, generalized Wilcoxon test, nonparametric Behrens-Fisher test, probabilistic index test	Kruskal-Wallis H test, one-way ANOVA on ranks, Kruskal-Wallis one-way analysis of variance, Kruskal-Wallis Testi
مرتبط	6	5
خلاصه	The Brunner-Munzel test is a nonparametric two-sample hypothesis test that estimates the probabilistic superiority index P(X < Y) — the probability that a randomly selected observation from one group exceeds a randomly selected observation from the other. Introduced by Brunner and Munzel in 2000 as a solution to the nonparametric Behrens-Fisher problem, it remains valid even when the two groups have unequal variances or differently shaped distributions, making it a robust alternative to the Mann-Whitney U test in heteroscedastic settings.	The Kruskal-Wallis H test is a nonparametric hypothesis test that compares three or more independent groups to decide whether their distributions (typically their medians) differ. Introduced by William Kruskal and W. Allen Wallis in 1952, it works on ranks rather than raw values and is the distribution-free counterpart to one-way ANOVA.