مقایسهٔ روشها
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| تحلیل کوواریانس (ANCOVA)× | Hotelling's T² Test× | تحلیل واریانس چندمتغیره (MANOVA)× | |
|---|---|---|---|
| حوزه | آمار | آمار | آمار |
| خانواده | Hypothesis test | Hypothesis test | Hypothesis test |
| سال پیدایش≠ | 1932 | 1931 | 1932 |
| پدیدآور≠ | Ronald A. Fisher | Harold Hotelling | Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.) |
| نوع≠ | Parametric group comparison with covariate control | Multivariate parametric mean comparison | Parametric multivariate mean comparison |
| منبع بنیادین≠ | Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574 | 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 |
| نامهای دیگر≠ | analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi) | Hotelling T² Testi — Çok Değişkenli t-Testi, multivariate t-test, Hotelling T-squared | Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA) |
| مرتبط≠ | 4 | 6 | 5 |
| خلاصه≠ | ANCOVA is a parametric hypothesis test that compares the adjusted means of two or more independent groups while statistically controlling for one or more continuous covariates. By removing the portion of outcome variance explained by the covariate, ANCOVA increases statistical precision and produces fairer group comparisons. The method builds on the general linear model framework consolidated by Fisher in the early 1930s and is described comprehensively by Tabachnick and Fidell (2013). | 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. |
| ScholarGateمجموعهداده ↗ |
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