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| Hotellingův T² test× | Multivariační analýza rozptylu (MANOVA)× | Mnohorozměrná vícenásobná lineární regrese× | |
|---|---|---|---|
| Obor | Statistika | Statistika | Statistika |
| Rodina≠ | Hypothesis test | Hypothesis test | Regression model |
| Rok vzniku≠ | 1931 | 1932 | 2007 |
| Tvůrce≠ | Harold Hotelling | Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.) | Johnson & Wichern (textbook treatment); classical multivariate least squares |
| Typ≠ | Multivariate parametric mean comparison | Parametric multivariate mean comparison | Multivariate linear regression |
| Původní zdroj≠ | Hotelling, H. (1931). The Generalization of Student's Ratio. Annals of Mathematical Statistics, 2(3), 360–378. link ↗ | 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 |
| Další názvy≠ | 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) |
| Příbuzné≠ | 6 | 5 | 5 |
| Shrnutí≠ | 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. |
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