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| Lilliefors 正态性检验× | 夏皮罗-威尔克正态性检验× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族≠ | Regression model | Hypothesis test |
| 起源年份≠ | 1967 | 1965 |
| 提出者≠ | Hubert W. Lilliefors | S. S. Shapiro & M. B. Wilk |
| 类型≠ | Goodness-of-fit / normality test | Normality (goodness-of-fit) test |
| 开创性文献≠ | Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown. Journal of the American Statistical Association, 62(318), 399-402. DOI ↗ | Shapiro, S. S. & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3-4), 591–611. DOI ↗ |
| 别名 | Lilliefors corrected Kolmogorov-Smirnov test, Lilliefors normality test, Lilliefors Testi | Shapiro-Wilk W test, W test for normality, Shapiro-Wilk normallik testi |
| 相关≠ | 5 | 2 |
| 摘要≠ | The Lilliefors test is a goodness-of-fit test that checks whether a continuous sample comes from a normal (or exponential) distribution when the mean and variance are unknown and estimated from the data. Introduced by Hubert W. Lilliefors in 1967, it adjusts the critical values of the Kolmogorov-Smirnov test so that they remain valid once the distribution's parameters are estimated rather than known in advance. | The Shapiro-Wilk test is a hypothesis test that checks whether a continuous variable was drawn from a normal distribution. It was introduced by Samuel Shapiro and Martin Wilk in 1965 and is regarded as one of the most powerful normality tests, recommended for sample sizes below 5000. |
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