เปรียบเทียบวิธี

	Robust ANOVA (Welch & Trimmed Mean)	การถดถอยกำลังสองน้อยที่สุดสามัญ (OLS)	การทดสอบการสับเปลี่ยน (การสุ่ม)	ตัวประมาณค่าแบบ Theil-Sen
สาขาวิชา	สถิติศาสตร์	เศรษฐมิติ	สถิติศาสตร์	สถิติศาสตร์
ตระกูล	Regression model	Regression model	Regression model	Regression model
ปีกำเนิด	1951	2019	2005	1968
ผู้ริเริ่ม	Welch (1951); robust trimmed-mean approach popularised by Wilcox	Wooldridge (textbook treatment); classical least squares	Good (2005); Edgington & Onghena (2007); resampling tradition	Henri Theil (1950); P. K. Sen (1968)
ประเภท	Robust one-way analysis of variance	Linear regression	Nonparametric resampling test	Robust linear regression
แหล่งต้นตำรับ	Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	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.
ชื่อเรียกอื่น	Welch ANOVA, trimmed-mean ANOVA, heteroscedastic one-way ANOVA, Robust ANOVA (Welch & Trimmed Mean)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	randomization test, exact permutation test, re-randomization test, Permütasyon Testi	Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator
ที่เกี่ยวข้อง	5	5	5	6
สรุป	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	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%.