Comparisons of various types of normality tests

Normality tests can be classified into tests based on chi-squared, moments, empirical distribution, spacings, regression and correlation and other special tests. This paper studies and compares the power of eight selected normality tests: the Shapiro-Wilk test, the Kolmogorov-Smirnov test, the Lilliefors test, the Cramer-von Mises test, the Anderson-Darling test, the D'Agostino-Pearson test, the Jarque-Bera test and chi-squared test. Power comparisons of these eight tests were obtained via the Monte Carlo simulation of sample data generated from alternative distributions that follow symmetric short-tailed, symmetric long-tailed and asymmetric distributions. Our simulation results show that for symmetric short-tailed distributions, D'Agostino and Shapiro-Wilk tests have better power. For symmetric long-tailed distributions, the power of Jarque-Bera and D'Agostino tests is quite comparable with the Shapiro-Wilk test. As for asymmetric distributions, the Shapiro-Wilk test is the most powerful test followed by the Anderson-Darling test.