In this article, we investigate the power of six standard goodness-of-fit tests of normality; several of these are sensitive to departures from normality in both skewness and kurtosis—the omnibus property. The power is estimated through simulation when the alternative is stable with α = 1.0(.3)1.9, β =.00(.25)1.00, and samples are of size n = 10, 20, 50, 100. The goodness-of-fit tests are based on the skewness statistic √b1, the kurtosis statistic b2, a joint test using √b1and b2, the Shapiro-Wilk W, the Studentized range test u, and the D’Agostino D. Our results indicate that the test based on b2is generally preferred if n ≥ 50 and β ≤.75. For the remaining configurations of n, α, and β, the test based on √b1is generally preferred.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty