مقایسهٔ روش‌ها

	ANOVAی ناپارامتریک (میانگین ناپارامتریک ولش و میانگین هرس‌شده)	استنتاج بوتسترپ	رگرسیون حداقل مربعات معمولی (OLS)	آزمون جایگشتی (تصادفی‌سازی)
حوزه	آمار	آمار	اقتصادسنجی	آمار
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	1951	1979	2019	2005
پدیدآور	Welch (1951); robust trimmed-mean approach popularised by Wilcox	Bradley Efron	Wooldridge (textbook treatment); classical least squares	Good (2005); Edgington & Onghena (2007); resampling tradition
نوع	Robust one-way analysis of variance	Resampling-based inference	Linear regression	Nonparametric resampling test
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	Good, P. (2005). Permutation, Parametric and Bootstrap Tests of Hypotheses (3rd ed.). Springer. ISBN: 978-0387202792
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	randomization test, exact permutation test, re-randomization test, Permütasyon Testi
مرتبط	5	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).	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.