方法对比

	多元方差分析 (MANOVA)	协方差分析 (ANCOVA)	独立样本t检验	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	1932	1932	1908	1925
提出者	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)	Ronald A. Fisher	Student (W. S. Gosset)	Ronald A. Fisher
类型	Parametric multivariate mean comparison	Parametric group comparison with covariate control	Parametric mean comparison	Parametric mean comparison
开创性文献	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574	Student (1908). The probable error of a mean. Biometrika, 6(1), 1–25.	Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.
别名	Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA)	analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi)	student t-test, two-sample t-test, unpaired t-test, bağımsız örneklem t-testi	one-factor ANOVA, single-factor ANOVA, analysis of variance, tek yönlü ANOVA
相关	5	4	4	4
摘要	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.	ANCOVA is a parametric hypothesis test that compares the adjusted means of two or more independent groups while statistically controlling for one or more continuous covariates. By removing the portion of outcome variance explained by the covariate, ANCOVA increases statistical precision and produces fairer group comparisons. The method builds on the general linear model framework consolidated by Fisher in the early 1930s and is described comprehensively by Tabachnick and Fidell (2013).	The independent samples t-test is a parametric hypothesis test that compares the means of two independent groups to decide whether they differ significantly. It builds on the t-distribution introduced by Student (W. S. Gosset) in 1908 and assumes the measured values are continuous, approximately normally distributed, and have equal variances.	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.