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| Phân tích Phương sai Đa biến (MANOVA)× | Phân tích hiệp phương sai (ANCOVA)× | Independent Samples t-test× | |
|---|---|---|---|
| Lĩnh vực | Thống kê | Thống kê | Thống kê |
| Họ | Hypothesis test | Hypothesis test | Hypothesis test |
| Năm ra đời≠ | 1932 | 1932 | 1908 |
| Người khởi xướng≠ | Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.) | Ronald A. Fisher | Student (W. S. Gosset) |
| Loại≠ | Parametric multivariate mean comparison | Parametric group comparison with covariate control | Parametric mean comparison |
| Công trình gốc≠ | Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574 | Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574 | Student (1908). The probable error of a mean. Biometrika, 6(1), 1–25. DOI ↗ |
| Tên gọi khác≠ | Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA) | analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi) | student t-test, two-sample t-test, unpaired t-test, bağımsız örneklem t-testi |
| Liên quan≠ | 5 | 4 | 4 |
| Tóm tắt≠ | 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. | 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). | 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. |
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