A test for departure from normality based on a biweight estimator of scale

Abstract

The ratio of two estimators of variance is proposed as a test statistic for comparing normal versus long-tailed symmetric or skewed alternatives. The 90, 95, 97.5 and 99th percentage points are found through extensive simulations, and approximations for the 90 and 95th percentage points are given. The proposed test is compared to the use of √ b 1 , b 2 , Shapiro & Wilk's W test. D'Agostino's test and Spiegelhalter's T' test. The proposed test outperforms all considered competitors for long-tailed symmetric alternatives and performs well for all other cases considered.