方法对比
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| 稳健方差分析（Welch & Trimmed Mean）× | Theil-Sen 估计器× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1951 | 1968 |
| 提出者≠ | Welch (1951); robust trimmed-mean approach popularised by Wilcox | Henri Theil (1950); P. K. Sen (1968) |
| 类型≠ | Robust one-way analysis of variance | Robust linear regression |
| 开创性文献≠ | Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336. DOI ↗ | Sen, P. K. (1968). Estimates of the Regression Coefficient Based on Kendall's Tau. Journal of the American Statistical Association, 63(324), 1379-1389. DOI ↗ |
| 别名 | Welch ANOVA, trimmed-mean ANOVA, heteroscedastic one-way ANOVA, Robust ANOVA (Welch & Trimmed Mean) | Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator |
| 相关≠ | 5 | 6 |
| 摘要≠ | Robust ANOVA compares the central tendency of three or more groups when the classical assumptions of normality and equal variances fail. It combines Welch's heteroscedasticity-adjusted statistic, introduced by Welch in 1951, with trimmed-mean tests advanced by Wilcox, giving reliable comparisons in the presence of outliers and unequal group spreads. | The Theil-Sen estimator is a robust linear regression method that estimates the slope as the median of the slopes computed over all pairs of data points. Introduced by Henri Theil in 1950 and extended by P. K. Sen in 1968, it tolerates outliers in the response with a breakdown point of about 29%. |
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