方法对比
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| 双向方差分析（Two-Way ANOVA）× | 协方差分析 (ANCOVA)× | 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≠ | 1925 | 1932 | 1932 |
| 提出者≠ | Ronald A. Fisher | Ronald A. Fisher | Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.) |
| 类型≠ | Parametric factorial mean comparison | Parametric group comparison with covariate control | Parametric multivariate mean comparison |
| 开创性文献≠ | Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley. ISBN: 978-1119113478 | 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 |
| 别名≠ | factorial ANOVA, two-factor ANOVA, İki Yönlü ANOVA | analysis of covariance, covariance analysis, ANCOVA (Kovaryans Analizi) | Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA) |
| 相关≠ | 6 | 4 | 5 |
| 摘要≠ | Two-Way ANOVA is a parametric hypothesis test that simultaneously examines the main effects of two independent categorical factors and their interaction effect on a single continuous dependent variable. The technique was developed within the broader framework of the analysis of variance established by Ronald A. Fisher in 1925 and remains the standard approach whenever an experiment or survey includes exactly two between-subjects factors. | 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). | 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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