方法对比

	双向方差分析（Two-Way ANOVA）	Kruskal-Wallis H检验	多元方差分析 (MANOVA)	单因素方差分析
领域	统计学	统计学	统计学	统计学
方法族	Hypothesis test	Hypothesis test	Hypothesis test	Hypothesis test
起源年份	1925	1952	1932	1925
提出者	Ronald A. Fisher	William Kruskal & W. Allen Wallis	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)	Ronald A. Fisher
类型	Parametric factorial mean comparison	Nonparametric group comparison	Parametric multivariate mean comparison	Parametric mean comparison
开创性文献	Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley. ISBN: 978-1119113478	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. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574	Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.
别名	factorial ANOVA, two-factor ANOVA, İki Yönlü ANOVA	Kruskal-Wallis H test, one-way ANOVA on ranks, Kruskal-Wallis one-way analysis of variance, Kruskal-Wallis Testi	Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA)	one-factor ANOVA, single-factor ANOVA, analysis of variance, tek yönlü ANOVA
相关	6	5	5	4
摘要	Two-Way ANOVA is a parametric hypothesis test that simultaneously examines the main effects of two independent categorical factors and their interaction effect on a single continuous dependent variable. The technique was developed within the broader framework of the analysis of variance established by Ronald A. Fisher in 1925 and remains the standard approach whenever an experiment or survey includes exactly two between-subjects factors.	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.	MANOVA is a parametric hypothesis test that simultaneously compares group means across multiple continuous dependent variables, controlling the inflation of Type I error that would result from running separate ANOVAs. Key multivariate test statistics — Wilks' Lambda, Pillai's Trace, Hotelling-Lawley Trace, and Roy's Greatest Root — were developed between the 1930s and 1950s, with Wilks' Lambda formalised by Samuel Stanley Wilks in 1932.	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.