方法对比
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| 判别分析× | Hotelling T²检验× | 多元方差分析 (MANOVA)× | |
|---|---|---|---|
| 领域 | 统计学 | 统计学 | 统计学 |
| 方法族≠ | Latent structure | Hypothesis test | Hypothesis test |
| 起源年份≠ | 1936 | 1931 | 1932 |
| 提出者≠ | Ronald A. Fisher | Harold Hotelling | Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.) |
| 类型≠ | Supervised classification and dimension reduction | Multivariate parametric mean comparison | Parametric multivariate mean comparison |
| 开创性文献≠ | Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2), 179–188. DOI ↗ | 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 |
| 别名≠ | LDA, Fisher discriminant analysis, discriminant function analysis, canonical discriminant analysis | Hotelling T² Testi — Çok Değişkenli t-Testi, multivariate t-test, Hotelling T-squared | Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA) |
| 相关≠ | 4 | 6 | 5 |
| 摘要≠ | Discriminant analysis finds linear combinations of predictor variables that best separate two or more known groups. It is used both to understand which predictors distinguish the groups and to classify new observations into those groups with minimum error. | 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. |
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