A modification of the test of Shapiro and Wilk for normality

The W statistic of Shapiro and Wilk provides the best omnibus test of normality but its application is limited up to n = 50. This study modifies W, such that it can be extended for all sample sizes. The critical values of (W) over tilde, i.e., the modification of W, is given for n up to 5000. The empirical moments show that the null distribution of (W) over tilde is skewed to the left and is consistent for all sample sizes. Empirical powers of (W) over tilde are also comparable with those of W.