手法を比較

	ホテリングのT²検定	共分散構造を持つ多変量分散分析（MANCOVA）	多変量重回帰分析
分野	統計学	統計学	統計学
系統	Hypothesis test	Hypothesis test	Regression model
提唱年	1931	1970	2007
提唱者	Harold Hotelling	Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s	Johnson & Wichern (textbook treatment); classical multivariate least squares
種類	Multivariate parametric mean comparison	Parametric multivariate mean comparison with covariate control	Multivariate linear regression
原典	Hotelling, H. (1931). The Generalization of Student's Ratio. Annals of Mathematical Statistics, 2(3), 360–378.	Tabachnick, B. G. & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson. ISBN: 978-0134790541	Johnson, R. A. & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (6th ed.). Pearson. ISBN: 978-0131877153
別名	Hotelling T² Testi — Çok Değişkenli t-Testi, multivariate t-test, Hotelling T-squared	MANCOVA, multivariate ANCOVA, MANOVA with covariates, MANCOVA — Çok Değişkenli Kovaryans Analizi	multivariate multiple regression, MLR with multiple dependent variables, multiple-outcome regression, Çok Değişkenli Regresyon (MLR — Çoklu DV)
関連	6	5	5
概要	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.	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).	Multivariate regression is a linear regression method that predicts several continuous dependent variables at the same time from a shared set of predictors. As developed in standard treatments such as Johnson and Wichern's Applied Multivariate Statistical Analysis (2007), each response equation can be fitted by ordinary least squares while the covariance structure of the residuals is used for joint testing across outcomes.