方法对比

	协方差多变量分析 (MANCOVA)	判别分析	Hotelling T²检验	多元方差分析 (MANOVA)
领域	统计学	统计学	统计学	统计学
方法族	Hypothesis test	Latent structure	Hypothesis test	Hypothesis test
起源年份	1970	1936	1931	1932
提出者	Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s	Ronald A. Fisher	Harold Hotelling	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)
类型	Parametric multivariate mean comparison with covariate control	Supervised classification and dimension reduction	Multivariate parametric mean comparison	Parametric multivariate mean comparison
开创性文献	Tabachnick, B. G. & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson. ISBN: 978-0134790541	Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2), 179–188.	Hotelling, H. (1931). The Generalization of Student's Ratio. Annals of Mathematical Statistics, 2(3), 360–378.	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574
别名	MANCOVA, multivariate ANCOVA, MANOVA with covariates, MANCOVA — Çok Değişkenli Kovaryans Analizi	LDA, Fisher discriminant analysis, discriminant function analysis, canonical discriminant analysis	Hotelling T² Testi — Çok Değişkenli t-Testi, multivariate t-test, Hotelling T-squared	Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA)
相关	5	4	6	5
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).	Discriminant analysis finds linear combinations of predictor variables that best separate two or more known groups. It is used both to understand which predictors distinguish the groups and to classify new observations into those groups with minimum error.	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.	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.