পদ্ধতির তুলনা করুন

	হোটেলিং-এর T² পরীক্ষা	স্বাধীন নমুনা টি-পরীক্ষা	মাল্টিভেরিয়েট অ্যানালাইসিস অফ ভ্যারিয়েন্স (MANOVA)	বহুমাত্রিক বহুচলক রৈখিক নির্ভরণ (Multivariate Multiple Linear Regression)
ক্ষেত্র	পরিসংখ্যান	পরিসংখ্যান	পরিসংখ্যান	পরিসংখ্যান
পরিবার	Hypothesis test	Hypothesis test	Hypothesis test	Regression model
উদ্ভবের বছর	1931	1908	1932	2007
প্রবর্তক	Harold Hotelling	Student (W. S. Gosset)	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)	Johnson & Wichern (textbook treatment); classical multivariate least squares
ধরন	Multivariate parametric mean comparison	Parametric mean comparison	Parametric multivariate mean comparison	Multivariate linear regression
মৌলিক উৎস	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	Johnson, R. A. & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (6th ed.). Pearson. ISBN: 978-0131877153
অপর নাম	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)	multivariate multiple regression, MLR with multiple dependent variables, multiple-outcome regression, Çok Değişkenli Regresyon (MLR — Çoklu DV)
সম্পর্কিত	6	4	5	5
সারসংক্ষেপ	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.	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.