A tool for systematically comparing the power of tests for normality
In this article, we describe a new approach to compare the power of different tests for normality. This approach provides the researcher with a practical tool for evaluating which test at their disposal is the most appropriate for their sampling problem. Using the Johnson systems of distribution, we estimate the power of a test for normality for any mean, variance, skewness, and kurtosis. Using this characterization and an innovative graphical representation, we validate our method by comparing three well-known tests for normality: the Pearson chi(2) test, the Kolmogorov-Smirnov test, and the D'Agostino-Pearson K(2) test. We obtain such comparison for a broad range of skewness, kurtosis, and sample sizes. We demonstrate that the D'Agostino-Pearson test gives greater power than the others against most of the alternative distributions and at most sample sizes. We also find that the Pearson chi(2) test gives greater power than Kolmogorov-Smirnov against most of the alternative distributions for sample sizes between 18 and 330.
test for normality graphical representation goodness of fit test johnson distributions comparison of powers skewness-kurtosis plane