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）	順列検定（ランダム化検定）
分野	統計学	統計学	統計学
系統	Regression model	Regression model	Regression model
提唱年	1948	1960	2005
提唱者	N. V. Smirnov	Howard Levene; Morton B. Brown and Alan B. Forsythe	Good (2005); Edgington & Onghena (2007); resampling tradition
種類	Nonparametric two-sample distribution test	Homogeneity of variance test (robust)	Nonparametric resampling test
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.	Good, P. (2005). Permutation, Parametric and Bootstrap Tests of Hypotheses (3rd ed.). Springer. ISBN: 978-0387202792
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	randomization test, exact permutation test, re-randomization test, Permütasyon Testi
関連	3	5	5
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 permutation test is a nonparametric resampling procedure that builds the sampling distribution of a test statistic directly from the data by repeatedly shuffling the group labels. Developed in the resampling tradition and treated systematically by Good (2005) and Edgington & Onghena (2007), it requires no parametric distributional assumption and yields an exact p-value.