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| Hotelling's T² Test× | t-тест за независими извадки× | Многовариантен анализ на ковариацията (MANCOVA)× | |
|---|---|---|---|
| Област | Статистика | Статистика | Статистика |
| Семейство | Hypothesis test | Hypothesis test | Hypothesis test |
| Година на възникване≠ | 1931 | 1908 | 1970 |
| Създател≠ | Harold Hotelling | Student (W. S. Gosset) | Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s |
| Тип≠ | Multivariate parametric mean comparison | Parametric mean comparison | Parametric multivariate mean comparison with covariate control |
| 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 ↗ | Tabachnick, B. G. & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson. ISBN: 978-0134790541 |
| 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 | MANCOVA, multivariate ANCOVA, MANOVA with covariates, MANCOVA — Çok Değişkenli Kovaryans Analizi |
| 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. | 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). |
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