Efficiency Comparisons of Normality Test Using Statistical Packages

The purpose of this study was to compare the efficiency of commercial statistical packages in testing normality. The six (6) tests being studies were Kolmogorov, Lilliefors and Shapiro-Wilk available in SPSS14 and Kolmogorov, Anderson-Darling and Ryan-Joiner available in MINITAB 14. The data for this study was obtained from simulation, by the method of Monte Carlo, under conditions of a normal distribution and slightly different from the normal distribution, by using Calc-Random Data menu of MINITAB 14. In each situation, 500 iterations were carried out with different sample size: 10, 20, 30, 50 and 100. Comparison of type I error rate and empirical power among the six test statistics were also made. It was found that Ryan-Joiner Test in MINITAB 14 had the highest empirical power in all cases and sample sizes, at a significance level of 0.10. The sample size of 100, in particular, showed the empirical power at almost 1. It also had an ability to control probability of Type I error in almost all situations under the criteria of Cochran. Nonetheless, the K-S test in MINITAB 14, appearing under the appellation of the K-S test was in fact the Lilliefors test.