مقایسهٔ روش‌ها

	ANOVAی ناپارامتریک (میانگین ناپارامتریک ولش و میانگین هرس‌شده)	استنتاج بوتسترپ	رگرسیون حداقل مربعات معمولی (OLS)
حوزه	آمار	آمار	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1951	1979	2019
پدیدآور	Welch (1951); robust trimmed-mean approach popularised by Wilcox	Bradley Efron	Wooldridge (textbook treatment); classical least squares
نوع	Robust one-way analysis of variance	Resampling-based inference	Linear regression
منبع بنیادین	Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.	Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics, 7(1), 1-26.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
نام‌های دیگر	Welch ANOVA, trimmed-mean ANOVA, heteroscedastic one-way ANOVA, Robust ANOVA (Welch & Trimmed Mean)	bootstrap, bootstrap resampling, nonparametric bootstrap, Bootstrap Çıkarımı	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
مرتبط	5	5	5
خلاصه	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.	Bootstrap inference, introduced by Bradley Efron in 1979, estimates the sampling distribution of a statistic by repeatedly resampling the observed data with replacement. It requires no distributional assumption and produces reliable confidence intervals even in small samples.	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).