مقایسهٔ روش‌ها

	آزمون H کروسکال-والیس	تحلیل کوواریانس چندمتغیره (MANCOVA)	تحلیل واریانس یک‌طرفه	آزمون تی ولش (واریانس‌های نابرابر)
حوزه	آمار	آمار	آمار	آمار
خانواده	Hypothesis test	Hypothesis test	Hypothesis test	Hypothesis test
سال پیدایش	1952	1970	1925	1947
پدیدآور	William Kruskal & W. Allen Wallis	Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s	Ronald A. Fisher	B. L. Welch
نوع	Nonparametric group comparison	Parametric multivariate mean comparison with covariate control	Parametric mean comparison	Parametric mean comparison (unequal variances)
منبع بنیادین	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	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.
نام‌های دیگر	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	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)
مرتبط	5	5	4	4
خلاصه	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).	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.