เปรียบเทียบวิธี

	การวิเคราะห์ความแปรปรวนร่วม (ANCOVA)	การทดสอบ T² ของ Hotelling	การวิเคราะห์ความแปรปรวนร่วม (Multivariate Analysis of Variance - MANOVA)
สาขาวิชา	สถิติศาสตร์	สถิติศาสตร์	สถิติศาสตร์
ตระกูล	Hypothesis test	Hypothesis test	Hypothesis test
ปีกำเนิด	1932	1931	1932
ผู้ริเริ่ม	Ronald A. Fisher	Harold Hotelling	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)
ประเภท	Parametric group comparison with covariate control	Multivariate parametric mean comparison	Parametric multivariate mean comparison
แหล่งต้นตำรับ	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.	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574
ชื่อเรียกอื่น	analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi)	Hotelling T² Testi — Çok Değişkenli t-Testi, multivariate t-test, Hotelling T-squared	Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA)
ที่เกี่ยวข้อง	4	6	5
สรุป	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.	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.