An Approximate Analysis of Variance Test for Normality

Abstract This article presents a modification of the Shapiro-Wilk W statistic for testing normality which can be used with large samples. Shapiro and Wilk gave coefficients and percentage points for sample sizes up to 50. These coefficients required obtaining an approximation to the covariance matrix of the normal order statistics. The proposed test uses coefficients which depend only on the expected values of the normal order statistics which are generally available. Results of an empirical sampling study to compare the sensitivity of the test statistic to the W test statistic are briefly discussed.