手法を比較

	ホテリングのT²検定	独立標本t検定	多変量分散分析 (MANOVA)
分野	統計学	統計学	統計学
系統	Hypothesis test	Hypothesis test	Hypothesis test
提唱年	1931	1908	1932
提唱者	Harold Hotelling	Student (W. S. Gosset)	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)
種類	Multivariate parametric mean comparison	Parametric mean comparison	Parametric multivariate mean comparison
原典	Hotelling, H. (1931). The Generalization of Student's Ratio. Annals of Mathematical Statistics, 2(3), 360–378.	Student (1908). The probable error of a mean. Biometrika, 6(1), 1–25.	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574
別名	Hotelling T² Testi — Çok Değişkenli t-Testi, multivariate t-test, Hotelling T-squared	student t-test, two-sample t-test, unpaired t-test, bağımsız örneklem t-testi	Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA)
関連	6	4	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.	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.	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.