A comparison of normality testing methods by empirical power and distribution of P -values

Normal distribution is commonly assumed distribution in statistical inference. Therefore, goodness-of-fit test for normality is required as a preliminary procedure in the applications. Most relevant testing methods have been evaluated using empirical power. However, the power depends on significance level, sample size, and alternative distributions. This study compares normality testing methods which have been verified excellent based on power, considering significance levels, sample sizes, and alternative distributions in addition to their powers. Furthermore we evaluate the performance of the testing methods using the expected and median values of p-values of the corresponding test statistics.