方法对比

	稳健方差分析（Welch & Trimmed Mean）	置换 (随机化) 检验	Theil-Sen 估计器
领域	统计学	统计学	统计学
方法族	Regression model	Regression model	Regression model
起源年份	1951	2005	1968
提出者	Welch (1951); robust trimmed-mean approach popularised by Wilcox	Good (2005); Edgington & Onghena (2007); resampling tradition	Henri Theil (1950); P. K. Sen (1968)
类型	Robust one-way analysis of variance	Nonparametric resampling test	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.	Good, P. (2005). Permutation, Parametric and Bootstrap Tests of Hypotheses (3rd ed.). Springer. ISBN: 978-0387202792	Sen, P. K. (1968). Estimates of the Regression Coefficient Based on Kendall's Tau. Journal of the American Statistical Association, 63(324), 1379-1389.
别名	Welch ANOVA, trimmed-mean ANOVA, heteroscedastic one-way ANOVA, Robust ANOVA (Welch & Trimmed Mean)	randomization test, exact permutation test, re-randomization test, Permütasyon Testi	Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator
相关	5	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 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.	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%.