مقایسهٔ روش‌ها

	آزمون برونر-مونزل	آزمون تی ولش (واریانس‌های نابرابر)
حوزه	آمار	آمار
خانواده	Hypothesis test	Hypothesis test
سال پیدایش	2000	1947
پدیدآور	Edgar Brunner & Ullrich Munzel	B. L. Welch
نوع	Nonparametric two-sample comparison	Parametric mean comparison (unequal variances)
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.	Welch, B. L. (1947). The generalization of Student's problem when several different population variances are involved. Biometrika, 34(1/2), 28–35.
نام‌های دیگر	Brunner-Munzel Testi, generalized Wilcoxon test, nonparametric Behrens-Fisher test, probabilistic index test	unequal variances t-test, Welch-Satterthwaite t-test, Welch t-Testi (Eşit Olmayan Varyans)
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.	Welch's t-test is a parametric hypothesis test that compares the means of two independent groups without assuming their variances are equal. It was introduced by B. L. Welch in 1947 as a more robust generalization of Student's two-sample test for situations where the two groups have different spread.