قارن الطرق

	اختبار برونر-مونزل	اختبار فليجنر-كيلين لتجانس التباينات
المجال	الإحصاء	الإحصاء
العائلة	Hypothesis test	Regression model
سنة النشأة	2000	1976
صاحب الطريقة	Edgar Brunner & Ullrich Munzel	Michael A. Fligner & Timothy J. Killeen
النوع	Nonparametric two-sample comparison	Rank-based test for homogeneity of variances
المصدر التأسيسي	Brunner, E. & Munzel, U. (2000). The Nonparametric Behrens-Fisher Problem: Asymptotic Theory and a Small-Sample Approximation. Biometrical Journal, 42(1), 17–25.	Fligner, M. A., & Killeen, T. J. (1976). Distribution-Free Two-Sample Tests for Scale. Journal of the American Statistical Association, 71(353), 210-213.
الأسماء البديلة	Brunner-Munzel Testi, generalized Wilcoxon test, nonparametric Behrens-Fisher test, probabilistic index test	Fligner-Killeen test of variance homogeneity, rank-based variance homogeneity test, Fligner-Killeen Varyans Homojenliği Testi
ذات صلة	6	5
الملخص	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 Fligner-Killeen test is a rank-based test that checks whether several independent groups share the same variance (scale). Introduced by Fligner and Killeen in 1976, it does not require the data to be normally distributed, making it a robust nonparametric alternative to the Levene and Bartlett tests.