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| Hotelling's T² Test× | t-тест за независими извадки× | Многовариантен множествен линеен регресионен анализ× | |
|---|---|---|---|
| Област | Статистика | Статистика | Статистика |
| Семейство≠ | Hypothesis test | Hypothesis test | Regression model |
| Година на възникване≠ | 1931 | 1908 | 2007 |
| Създател≠ | Harold Hotelling | Student (W. S. Gosset) | Johnson & Wichern (textbook treatment); classical multivariate least squares |
| Тип≠ | Multivariate parametric mean comparison | Parametric mean comparison | Multivariate linear regression |
| Основополагащ източник≠ | Hotelling, H. (1931). The Generalization of Student's Ratio. Annals of Mathematical Statistics, 2(3), 360–378. link ↗ | Student (1908). The probable error of a mean. Biometrika, 6(1), 1–25. DOI ↗ | Johnson, R. A. & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (6th ed.). Pearson. ISBN: 978-0131877153 |
| Други названия≠ | 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 multiple regression, MLR with multiple dependent variables, multiple-outcome regression, Çok Değişkenli Regresyon (MLR — Çoklu DV) |
| Свързани≠ | 6 | 4 | 5 |
| Резюме≠ | 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. | 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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