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| Test Bruno-Munzela× | Test H Kruskala-Wallisa× | |
|---|---|---|
| Dziedzina | Statystyka | Statystyka |
| Rodzina | Hypothesis test | Hypothesis test |
| Rok powstania≠ | 2000 | 1952 |
| Twórca≠ | Edgar Brunner & Ullrich Munzel | William Kruskal & W. Allen Wallis |
| Typ≠ | Nonparametric two-sample comparison | Nonparametric group comparison |
| Źródło pierwotne≠ | Brunner, E. & Munzel, U. (2000). The Nonparametric Behrens-Fisher Problem: Asymptotic Theory and a Small-Sample Approximation. Biometrical Journal, 42(1), 17–25. DOI ↗ | 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. DOI ↗ |
| Inne nazwy | 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 |
| Pokrewne≠ | 6 | 5 |
| Podsumowanie≠ | 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. |
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