قارن الطرق

	اختبار T² لهوتيلينج	تحليل التباين متعدد المتغيرات (MANOVA)	الانحدار الخطي المتعدد متعدد المتغيرات
المجال	الإحصاء	الإحصاء	الإحصاء
العائلة	Hypothesis test	Hypothesis test	Regression model
سنة النشأة	1931	1932	2007
صاحب الطريقة	Harold Hotelling	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)	Johnson & Wichern (textbook treatment); classical multivariate least squares
النوع	Multivariate parametric mean comparison	Parametric multivariate mean comparison	Multivariate linear regression
المصدر التأسيسي	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	Johnson, R. A. & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (6th ed.). Pearson. ISBN: 978-0131877153
الأسماء البديلة	Hotelling T² Testi — Çok Değişkenli t-Testi, multivariate t-test, Hotelling T-squared	Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA)	multivariate multiple regression, MLR with multiple dependent variables, multiple-outcome regression, Çok Değişkenli Regresyon (MLR — Çoklu DV)
ذات صلة	6	5	5
الملخص	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.	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.