مقایسهٔ روش‌ها

	تحلیل واریانس ولچ	آزمون H کروسکال-والیس	تحلیل واریانس یک‌طرفه
حوزه	آمار	آمار	آمار
خانواده	Hypothesis test	Hypothesis test	Hypothesis test
سال پیدایش	1951	1952	1925
پدیدآور	B. L. Welch	William Kruskal & W. Allen Wallis	Ronald A. Fisher
نوع	Parametric mean comparison (heteroscedastic)	Nonparametric group comparison	Parametric mean comparison
منبع بنیادین	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.	Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.
نام‌های دیگر	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	one-factor ANOVA, single-factor ANOVA, analysis of variance, tek yönlü ANOVA
مرتبط	3	5	4
خلاصه	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.	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.