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| Phân tích phương sai hai yếu tố (Two-Way ANOVA)× | Kiểm định H Kruskal-Wallis× | Phân tích Phương sai Đa biến (MANOVA)× | |
|---|---|---|---|
| Lĩnh vực | Thống kê | Thống kê | Thống kê |
| Họ | Hypothesis test | Hypothesis test | Hypothesis test |
| Năm ra đời≠ | 1925 | 1952 | 1932 |
| Người khởi xướng≠ | Ronald A. Fisher | William Kruskal & W. Allen Wallis | Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.) |
| Loại≠ | Parametric factorial mean comparison | Nonparametric group comparison | Parametric multivariate mean comparison |
| Công trình gốc≠ | Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley. ISBN: 978-1119113478 | Kruskal, W. H. & Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583–621. DOI ↗ | Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574 |
| Tên gọi khác≠ | factorial ANOVA, two-factor ANOVA, İki Yönlü ANOVA | Kruskal-Wallis H test, one-way ANOVA on ranks, Kruskal-Wallis one-way analysis of variance, Kruskal-Wallis Testi | Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA) |
| Liên quan≠ | 6 | 5 | 5 |
| Tóm tắt≠ | 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. | The Kruskal-Wallis H test is a nonparametric hypothesis test that compares three or more independent groups to decide whether their distributions (typically their medians) differ. Introduced by William Kruskal and W. Allen Wallis in 1952, it works on ranks rather than raw values and is the distribution-free counterpart to one-way ANOVA. | 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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