Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique

Abstract

In Statistics, test of normality is of great importance and cannot be neglected in statistical analysis. However, there exist many techniques for such analysis and researchers usually face with the choice of test. From the literature, it has been established that power of test of normality vary significantly based on sample sizes. In this study, seven normality tests were reviewed and the classification into LMP and UMP were based on Power-of-Test. The test of hypothesis was done at 5% level of significance. The tests considered as; Shapiro-Wilk, Anderson-Darling, Bonett-Serial, Robust Jarque-Bera, Skewness, Lilliefors and Kurtosis tests. The sample sizes considered are 10, 20, 50 and 100 with 1000 replicates. Simulation was done from 3 distributions namely, normal, gamma and beta distributions. It was found that all methods were stronger for the detection of normality when normal distribution was used but the variation in their power was obvious when non-normal distributions were used. Among the methods, only three can be referred to as UMP while the rest are LMP. The UMP methods are Shapiro-Wilk, Anderson-Darling and Lilliefors as their Power-of-Test was not affected by sample sizes.