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| Kiểm định Levene và Brown-Forsythe về sự bằng nhau của phương sai× | Kiểm định U Mann-Whitney× | Kiểm định hoán vị (Ngẫu nhiên hóa)× | |
|---|---|---|---|
| Lĩnh vực | Thống kê | Thống kê | Thống kê |
| Họ≠ | Regression model | Hypothesis test | Regression model |
| Năm ra đời≠ | 1960 | 1947 | 2005 |
| Người khởi xướng≠ | Howard Levene; Morton B. Brown and Alan B. Forsythe | H. B. Mann & D. R. Whitney | Good (2005); Edgington & Onghena (2007); resampling tradition |
| Loại≠ | Homogeneity of variance test (robust) | Nonparametric two-group comparison | Nonparametric resampling test |
| Công trình gốc≠ | Levene, H. (1960). Robust Tests for Equality of Variances. In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford University Press. link ↗ | Mann, H. B. & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18(1), 50–60. DOI ↗ | Good, P. (2005). Permutation, Parametric and Bootstrap Tests of Hypotheses (3rd ed.). Springer. ISBN: 978-0387202792 |
| Tên gọi khác≠ | Levene test, Brown-Forsythe test, homogeneity of variance test, Levene ve Brown-Forsythe Varyans Testi | Mann-Whitney-Wilcoxon test, Wilcoxon rank-sum test, Mann-Whitney U Testi | randomization test, exact permutation test, re-randomization test, Permütasyon Testi |
| Liên quan≠ | 5 | 4 | 5 |
| Tóm tắt≠ | The Levene and Brown-Forsythe test checks whether two or more groups share the same variance (homogeneity of variance). Levene (1960) built the test on absolute deviations from each group mean, and Brown and Forsythe (1974) made it robust to non-normal data by centring on the group median instead. | The Mann-Whitney U test is the nonparametric alternative to the independent samples t-test, comparing two independent groups by ranking all observations together rather than relying on their means. It was introduced by H. B. Mann and D. R. Whitney in 1947 and does not require the data to be normally distributed. | The permutation test is a nonparametric resampling procedure that builds the sampling distribution of a test statistic directly from the data by repeatedly shuffling the group labels. Developed in the resampling tradition and treated systematically by Good (2005) and Edgington & Onghena (2007), it requires no parametric distributional assumption and yields an exact p-value. |
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