手法を比較

	2標本コルモゴロフ・スミルノフ検定	Levene検定およびBrown-Forsythe検定（分散の等質性）	マン・ホイットニーのU検定
分野	統計学	統計学	統計学
系統	Regression model	Regression model	Hypothesis test
提唱年	1948	1960	1947
提唱者	N. V. Smirnov	Howard Levene; Morton B. Brown and Alan B. Forsythe	H. B. Mann & D. R. Whitney
種類	Nonparametric two-sample distribution test	Homogeneity of variance test (robust)	Nonparametric two-group comparison
原典	Smirnov, N. V. (1948). Table for Estimating the Goodness of Fit of Empirical Distributions. Annals of Mathematical Statistics, 19(2), 279-281.	Levene, H. (1960). Robust Tests for Equality of Variances. In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford University Press.	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.
別名	KS two-sample test, two-sample KS test, İki Örneklem Kolmogorov-Smirnov Testi	Levene test, Brown-Forsythe test, homogeneity of variance test, Levene ve Brown-Forsythe Varyans Testi	Mann-Whitney-Wilcoxon test, Wilcoxon rank-sum test, Mann-Whitney U Testi
関連	3	5	4
概要	The two-sample Kolmogorov-Smirnov test is a nonparametric procedure that asks whether two independent groups are drawn from the same continuous distribution. Building on Smirnov's 1948 tables, it compares the empirical cumulative distribution functions (CDFs) of the two samples and uses their maximum absolute distance as the test statistic.	The Levene and Brown-Forsythe test checks whether two or more groups share the same variance (homogeneity of variance). Levene (1960) built the test on absolute deviations from each group mean, and Brown and Forsythe (1974) made it robust to non-normal data by centring on the group median instead.	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.