手法を比較

	Welchの分散分析	一元配置分散分析	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	1951	1925	1947
提唱者	B. L. Welch	Ronald A. Fisher	B. L. Welch
種類	Parametric mean comparison (heteroscedastic)	Parametric mean comparison	Parametric mean comparison (unequal variances)
原典	Welch, B.L. (1951). On the Comparison of Several Mean Values. Biometrika, 38(3/4), 330–336.	Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.	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	Welch's F-test, heteroscedastic one-way ANOVA, Welch ANOVA — Heterojen Varyans ANOVA	one-factor ANOVA, single-factor ANOVA, analysis of variance, tek yönlü ANOVA	unequal variances t-test, Welch-Satterthwaite t-test, Welch t-Testi (Eşit Olmayan Varyans)
関連	3	4	4
概要	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.	One-way ANOVA is a parametric hypothesis test that compares the means of three or more independent groups on a single continuous outcome to decide whether at least one group mean differs. It rests on the variance-partitioning framework introduced by Ronald A. Fisher in 1925.	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.