方法对比

	协方差分析 (ANCOVA)	协方差多变量分析 (MANCOVA)	Welch's t检验（方差不齐）
领域	统计学	统计学	统计学
方法族	Hypothesis test	Hypothesis test	Hypothesis test
起源年份	1932	1970	1947
提出者	Ronald A. Fisher	Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s	B. L. Welch
类型	Parametric group comparison with covariate control	Parametric multivariate mean comparison with covariate control	Parametric mean comparison (unequal variances)
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. (2019). Using Multivariate Statistics (7th ed.). Pearson. ISBN: 978-0134790541	Welch, B. L. (1947). The generalization of Student's problem when several different population variances are involved. Biometrika, 34(1/2), 28–35.
别名	analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi)	MANCOVA, multivariate ANCOVA, MANOVA with covariates, MANCOVA — Çok Değişkenli Kovaryans Analizi	unequal variances t-test, Welch-Satterthwaite t-test, Welch t-Testi (Eşit Olmayan Varyans)
相关	4	5	4
摘要	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).	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).	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.