Comparison of power for the D'Agostino and the Wilk-Shapiro test of normality for small and moderate samples

Summary Results are given of a sampling study of the sensitivities of two statistical procedures viz. the D'A gostino and the W ilk -S hapiro test of normality. Four alternative distributions were considered. For 5 small sample sizes the test of D'A gostino seems to be clearly dominated by the W ilk -S hapiro test for each of the 4 alternatives. For sample size n = 100 the recently developed approximate W ilk -S hapiro test seems to dominate the D'A gostino test for the U -shaped distribution; however, little can be said about the difference in power of these two tests for the other 3 alternatives. Random samples generated from the standard normal distribution showed the degree of approximation of the percentiles of each test procedure to be good.