方法对比
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| 独立样本t检验× | 协方差多变量分析 (MANCOVA)× | 多元方差分析 (MANOVA)× | |
|---|---|---|---|
| 领域 | 统计学 | 统计学 | 统计学 |
| 方法族 | Hypothesis test | Hypothesis test | Hypothesis test |
| 起源年份≠ | 1908 | 1970 | 1932 |
| 提出者≠ | Student (W. S. Gosset) | Extension of MANOVA and ANCOVA traditions; consolidated in multivariate textbooks by the 1970s–1980s | Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.) |
| 类型≠ | Parametric mean comparison | Parametric multivariate mean comparison with covariate control | Parametric multivariate mean comparison |
| 开创性文献≠ | 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 | Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574 |
| 别名≠ | 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 | Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA) |
| 相关≠ | 4 | 5 | 5 |
| 摘要≠ | 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). | 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. |
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