方法对比

	协方差多变量分析 (MANCOVA)	协方差分析 (ANCOVA)	Hotelling T²检验
领域	统计学	统计学	统计学
方法族	Hypothesis test	Hypothesis test	Hypothesis test
起源年份	1970	1932	1931
提出者	Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s	Ronald A. Fisher	Harold Hotelling
类型	Parametric multivariate mean comparison with covariate control	Parametric group comparison with covariate control	Multivariate parametric mean comparison
开创性文献	Tabachnick, B. G. & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson. ISBN: 978-0134790541	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574	Hotelling, H. (1931). The Generalization of Student's Ratio. Annals of Mathematical Statistics, 2(3), 360–378.
别名	MANCOVA, multivariate ANCOVA, MANOVA with covariates, MANCOVA — Çok Değişkenli Kovaryans Analizi	analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi)	Hotelling T² Testi — Çok Değişkenli t-Testi, multivariate t-test, Hotelling T-squared
相关	5	4	6
摘要	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).	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).	Hotelling's T² test is a multivariate parametric hypothesis test that simultaneously compares the mean vectors of two independent groups across multiple continuous outcome variables. It was introduced by Harold Hotelling in 1931 as the direct multivariate generalization of Student's t-test, replacing the scalar mean difference with a vector difference scaled by the pooled variance-covariance matrix.