مقایسهٔ روش‌ها

	تحلیل کوواریانس چندمتغیره (MANCOVA)	تحلیل کوواریانس (ANCOVA)	تحلیل تمایز	تحلیل واریانس چندمتغیره (MANOVA)
حوزه	آمار	آمار	آمار	آمار
خانواده	Hypothesis test	Hypothesis test	Latent structure	Hypothesis test
سال پیدایش	1970	1932	1936	1932
پدیدآور	Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s	Ronald A. Fisher	Ronald A. Fisher	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)
نوع	Parametric multivariate mean comparison with covariate control	Parametric group comparison with covariate control	Supervised classification and dimension reduction	Parametric multivariate mean comparison
منبع بنیادین	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	Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2), 179–188.	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574
نام‌های دیگر	MANCOVA, multivariate ANCOVA, MANOVA with covariates, MANCOVA — Çok Değişkenli Kovaryans Analizi	analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi)	LDA, Fisher discriminant analysis, discriminant function analysis, canonical discriminant analysis	Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA)
مرتبط	5	4	4	5
خلاصه	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).	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.	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.