เปรียบเทียบวิธี

	ระยะมาฮาลาโนบิสแบบคงทน	แผนภาพกล่องปรับแก้สำหรับการแจกแจงแบบเบ้	การถดถอยกำลังสองตัดแต่งน้อยที่สุด (Least Trimmed Squares: LTS)	การประมาณค่าส่วนเบี่ยงเบนสัมบูรณ์มัธยฐาน (MAD)	Robust ANOVA (Welch & Trimmed Mean)
สาขาวิชา	สถิติศาสตร์	สถิติศาสตร์	สถิติศาสตร์	สถิติศาสตร์	สถิติศาสตร์
ตระกูล	Regression model	Regression model	Regression model	Regression model	Regression model
ปีกำเนิด	1990	2008	1984	1974	1951
ผู้ริเริ่ม	Rousseeuw & Van Zomeren (robust distance); Filzmoser, Garrett & Reimann (multivariate outlier detection)	Hubert & Vandervieren	Peter J. Rousseeuw	Hampel (influence-curve treatment); classical robust statistics	Welch (1951); robust trimmed-mean approach popularised by Wilcox
ประเภท	Robust multivariate outlier detection	Robust outlier detection / descriptive visualization	Robust linear regression	Robust scale estimator	Robust one-way analysis of variance
แหล่งต้นตำรับ	Rousseeuw, P. J. & Van Zomeren, B. C. (1990). Unmasking Multivariate Outliers and Leverage Points. Journal of the American Statistical Association, 85(411), 633-639.	Hubert, M. & Vandervieren, E. (2008). An Adjusted Boxplot for Skewed Distributions. Computational Statistics & Data Analysis, 52(12), 5186-5201.	Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871-880.	Hampel, F. R. (1974). The Influence Curve and Its Role in Robust Estimation. Journal of the American Statistical Association, 69(346), 383-393.	Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.
ชื่อเรียกอื่น	MCD Mahalanobis distance, robust mahalanobis, minimum covariance determinant distance, Robust Mahalanobis Uzaklığı	adjusted box plot, medcouple boxplot, skewness-adjusted boxplot, Düzeltilmiş Kutu Grafiği (Adjusted Boxplot)	LTS, least trimmed squares regression, trimmed least squares, robust regression	median absolute deviation, MAD scale estimator, robust scale estimation, Medyan Mutlak Sapma (MAD) Tahmini	Welch ANOVA, trimmed-mean ANOVA, heteroscedastic one-way ANOVA, Robust ANOVA (Welch & Trimmed Mean)
ที่เกี่ยวข้อง	5	5	5	5	5
สรุป	Robust Mahalanobis Distance flags multivariate outliers by measuring how far each observation lies from the centre of the data using a robust covariance estimate. It builds on the robust-distance framework of Rousseeuw and Van Zomeren (1990) and the multivariate outlier-detection approach of Filzmoser, Garrett and Reimann (2005), replacing the classical mean and covariance with the Minimum Covariance Determinant (MCD) estimate so that the outliers themselves do not distort the distance.	The Adjusted Boxplot is a robust descriptive tool introduced by Hubert and Vandervieren (2008) that corrects the classical IQR-based boxplot for skewness using the medcouple statistic, reducing the false labelling of outliers in asymmetric data.	Least Trimmed Squares is a robust linear regression method introduced by Peter J. Rousseeuw in 1984. Instead of fitting all residuals, it estimates the coefficients by minimising the sum of only the h smallest squared residuals, which gives it a breakdown point of up to 50% and reliable estimates on data heavily contaminated by outliers.	Median Absolute Deviation estimation is a robust measure of statistical dispersion that replaces the standard deviation when outliers are present. Rooted in the influence-curve framework formalised by Hampel (1974), it summarises the spread of a continuous variable using medians instead of means, so a single extreme value cannot distort the result.	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.