方法对比

	协方差分析 (ANCOVA)	Kruskal-Wallis H检验	Welch's t检验（方差不齐）
领域	统计学	统计学	统计学
方法族	Hypothesis test	Hypothesis test	Hypothesis test
起源年份	1932	1952	1947
提出者	Ronald A. Fisher	William Kruskal & W. Allen Wallis	B. L. Welch
类型	Parametric group comparison with covariate control	Nonparametric group comparison	Parametric mean comparison (unequal variances)
开创性文献	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574	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.	Welch, B. L. (1947). The generalization of Student's problem when several different population variances are involved. Biometrika, 34(1/2), 28–35.
别名	analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi)	Kruskal-Wallis H test, one-way ANOVA on ranks, Kruskal-Wallis one-way analysis of variance, Kruskal-Wallis Testi	unequal variances t-test, Welch-Satterthwaite t-test, Welch t-Testi (Eşit Olmayan Varyans)
相关	4	5	4
摘要	ANCOVA is a parametric hypothesis test that compares the adjusted means of two or more independent groups while statistically controlling for one or more continuous covariates. By removing the portion of outcome variance explained by the covariate, ANCOVA increases statistical precision and produces fairer group comparisons. The method builds on the general linear model framework consolidated by Fisher in the early 1930s and is described comprehensively by Tabachnick and Fidell (2013).	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.	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.