مقایسهٔ روش‌ها

	آزمون برونر-مونزل	آزمون رتبه علامت‌دار ویلکاکسون
حوزه	آمار	آمار
خانواده	Hypothesis test	Hypothesis test
سال پیدایش	2000	1945
پدیدآور	Edgar Brunner & Ullrich Munzel	Frank Wilcoxon
نوع	Nonparametric two-sample comparison	Nonparametric paired 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.	Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83.
نام‌های دیگر	Brunner-Munzel Testi, generalized Wilcoxon test, nonparametric Behrens-Fisher test, probabilistic index test	Wilcoxon matched-pairs signed-rank test, signed-rank test, Wilcoxon İşaretli Sıra Testi
مرتبط	6	4
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 Wilcoxon signed-rank test is the nonparametric alternative to the paired t-test, comparing two related measurements on the same subjects to decide whether their typical difference is zero. It was introduced by Frank Wilcoxon in 1945 and works on continuous or ordinal data without assuming normality.