手法を比較

	2標本コルモゴロフ・スミルノフ検定	マン・ホイットニーのU検定	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	Hypothesis test	Regression model
提唱年	1948	1947	2005
提唱者	N. V. Smirnov	H. B. Mann & D. R. Whitney	Good (2005); Edgington & Onghena (2007); resampling tradition
種類	Nonparametric two-sample distribution test	Nonparametric two-group comparison	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.	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.	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	Mann-Whitney-Wilcoxon test, Wilcoxon rank-sum test, Mann-Whitney U Testi	randomization test, exact permutation test, re-randomization test, Permütasyon Testi
関連	3	4	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 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.	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.