手法を比較

	クラスカル・ウォリス H検定	共分散構造を持つ多変量分散分析（MANCOVA）	Welchのt検定（等分散を仮定しない）
分野	統計学	統計学	統計学
系統	Hypothesis test	Hypothesis test	Hypothesis test
提唱年	1952	1970	1947
提唱者	William Kruskal & W. Allen Wallis	Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s	B. L. Welch
種類	Nonparametric group comparison	Parametric multivariate mean comparison with covariate control	Parametric mean comparison (unequal variances)
原典	Kruskal, W. H. & Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583–621.	Tabachnick, B. G. & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson. ISBN: 978-0134790541	Welch, B. L. (1947). The generalization of Student's problem when several different population variances are involved. Biometrika, 34(1/2), 28–35.
別名	Kruskal-Wallis H test, one-way ANOVA on ranks, Kruskal-Wallis one-way analysis of variance, Kruskal-Wallis Testi	MANCOVA, multivariate ANCOVA, MANOVA with covariates, MANCOVA — Çok Değişkenli Kovaryans Analizi	unequal variances t-test, Welch-Satterthwaite t-test, Welch t-Testi (Eşit Olmayan Varyans)
関連	5	5	4
概要	The Kruskal-Wallis H test is a nonparametric hypothesis test that compares three or more independent groups to decide whether their distributions (typically their medians) differ. Introduced by William Kruskal and W. Allen Wallis in 1952, it works on ranks rather than raw values and is the distribution-free counterpart to one-way ANOVA.	MANCOVA (Multivariate Analysis of Covariance) is a parametric hypothesis test that simultaneously compares two or more groups on multiple continuous dependent variables while statistically controlling for one or more covariates. It extends MANOVA by incorporating covariate adjustment, a tradition consolidated in multivariate statistical methodology by the 1970s and authoritatively documented by Tabachnick and Fidell (2019).	Welch's t-test is a parametric hypothesis test that compares the means of two independent groups without assuming their variances are equal. It was introduced by B. L. Welch in 1947 as a more robust generalization of Student's two-sample test for situations where the two groups have different spread.