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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, i.e. the modification of W, is given for n up to 5000. The empirical moments show that the null distribution of W is skewed to the left and is consistant for all sample sizes. Empirical powers of W are also comparable with those of W.
Rahman et al. (Tue,) studied this question.