مقایسهٔ روش‌ها

	آزمون سیگل-توکی برای تفاوت‌های مقیاس	آزمون فِلِینِر-کیلین برای همگنی واریانس‌ها	آزمون یو مان-ویتنی
حوزه	آمار	آمار	آمار
خانواده	Hypothesis test	Regression model	Hypothesis test
سال پیدایش	1960	1976	1947
پدیدآور	Sidney Siegel & John W. Tukey	Michael A. Fligner & Timothy J. Killeen	H. B. Mann & D. R. Whitney
نوع	Nonparametric scale comparison	Rank-based test for homogeneity of variances	Nonparametric two-group comparison
منبع بنیادین	Siegel, S. & Tukey, J. W. (1960). A Nonparametric Sum of Ranks Procedure for Relative Spread in Unpaired Samples. Journal of the American Statistical Association, 55(291), 429–444.	Fligner, M. A., & Killeen, T. J. (1976). Distribution-Free Two-Sample Tests for Scale. Journal of the American Statistical Association, 71(353), 210-213.	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.
نام‌های دیگر	Siegel-Tukey rank test, nonparametric scale test, Siegel-Tukey Testi — Ölçek Farklılığı	Fligner-Killeen test of variance homogeneity, rank-based variance homogeneity test, Fligner-Killeen Varyans Homojenliği Testi	Mann-Whitney-Wilcoxon test, Wilcoxon rank-sum test, Mann-Whitney U Testi
مرتبط	2	5	4
خلاصه	The Siegel-Tukey test is a nonparametric hypothesis test that detects differences in variability (spread) between two independent groups whose central tendencies are equal or have been equalised. Introduced by Sidney Siegel and John W. Tukey in 1960, it is the nonparametric counterpart of Levene's test and requires no assumption of normality.	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.	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.