方法对比
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| 双样本柯尔莫哥洛夫-斯米尔诺夫检验× | Levene 和 Brown-Forsythe 方差齐性检验× | Mann-Whitney U 检验× | |
|---|---|---|---|
| 领域 | 统计学 | 统计学 | 统计学 |
| 方法族≠ | Regression model | Regression model | Hypothesis test |
| 起源年份≠ | 1948 | 1960 | 1947 |
| 提出者≠ | N. V. Smirnov | Howard Levene; Morton B. Brown and Alan B. Forsythe | H. B. Mann & D. R. Whitney |
| 类型≠ | Nonparametric two-sample distribution test | Homogeneity of variance test (robust) | Nonparametric two-group comparison |
| 开创性文献≠ | Smirnov, N. V. (1948). Table for Estimating the Goodness of Fit of Empirical Distributions. Annals of Mathematical Statistics, 19(2), 279-281. DOI ↗ | 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 ↗ |
| 别名≠ | KS two-sample test, two-sample KS test, İki Örneklem Kolmogorov-Smirnov Testi | 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 |
| 相关≠ | 3 | 5 | 4 |
| 摘要≠ | The two-sample Kolmogorov-Smirnov test is a nonparametric procedure that asks whether two independent groups are drawn from the same continuous distribution. Building on Smirnov's 1948 tables, it compares the empirical cumulative distribution functions (CDFs) of the two samples and uses their maximum absolute distance as the test statistic. | 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. |
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