So sánh phương pháp

	Kiểm định Brunner-Munzel	Kiểm định U Mann-Whitney
Lĩnh vực	Thống kê	Thống kê
Họ	Hypothesis test	Hypothesis test
Năm ra đời	2000	1947
Người khởi xướng	Edgar Brunner & Ullrich Munzel	H. B. Mann & D. R. Whitney
Loại	Nonparametric two-sample comparison	Nonparametric two-group comparison
Công trình gốc	Brunner, E. & Munzel, U. (2000). The Nonparametric Behrens-Fisher Problem: Asymptotic Theory and a Small-Sample Approximation. Biometrical Journal, 42(1), 17–25.	Mann, H. B. & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18(1), 50–60.
Tên gọi khác	Brunner-Munzel Testi, generalized Wilcoxon test, nonparametric Behrens-Fisher test, probabilistic index test	Mann-Whitney-Wilcoxon test, Wilcoxon rank-sum test, Mann-Whitney U Testi
Liên quan	6	4
Tóm tắt	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 Mann-Whitney U test is the nonparametric alternative to the independent samples t-test, comparing two independent groups by ranking all observations together rather than relying on their means. It was introduced by H. B. Mann and D. R. Whitney in 1947 and does not require the data to be normally distributed.