方法对比

	Welch方差分析	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	1951	1952	1947
提出者	B. L. Welch	William Kruskal & W. Allen Wallis	B. L. Welch
类型	Parametric mean comparison (heteroscedastic)	Nonparametric group comparison	Parametric mean comparison (unequal variances)
开创性文献	Welch, B.L. (1951). On the Comparison of Several Mean Values. Biometrika, 38(3/4), 330–336.	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	Welch's F-test, heteroscedastic one-way ANOVA, Welch ANOVA — Heterojen Varyans ANOVA	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	3	5	4
摘要	Welch ANOVA is a parametric hypothesis test that compares the means of three or more independent groups when their variances are not equal. Introduced by B. L. Welch in 1951, it replaces classic one-way ANOVA whenever the homogeneity-of-variance assumption fails, while still requiring approximately normal data.	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.