A Comparative Study of Various Tests for Normality

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Abstract
Results are given of an empirical sampling study of the sensitivities of nine statistical procedures for evaluating the normality of a complete sample. The nine statistics are W (Shapiro and Wilk, 1965), (standard third moment), b 2 (standard fourth moment), KS (Kolmogorov-Smirnov), CM (Cramer-Von Mises), WCM (weighted CM), D (modified KS), CS (chi-squared) and u (Studentized range). Forty-five alternative distributions in twelve families and five sample sizes were studied. Results are included on the comparison of the statistical procedures in relation to groupings of the alternative distributions, on means and variances of the statistics under the various alternatives, on dependence of sensitivities on sample size, on approach to normality as measured by the W statistic within some classes of distribution, and on the effect of misspecification of parameters on the performance of the simple hypothesis test statistics. The general findings include: (i) The W statistic provides a generally superio...

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