Investigation of Some Univariate Normality Tests in Terms of Type-I Errors and Test Power

Abstract

In this study, Shapiro-Wilk, Kolmogorov-Smirnov, Skewness, Kurtosis, Lilliefors, Jargue-Bera and D'Agostino -Pearson tests, which are univariate normality tests, were compared in point of type-I error and power performances. For comparisons, samples were created in various distributions and sample volumes by simulation technique, and the probability of type-I error was taken as 0.05 in comparisons. Thus, it is aimed to determine the best test to check whether the normality condition is met in univariate data. As a result of the comparison, it was determined that the Jargue-Bera test gave better results than the other tests in point of type-I error probability. In addition, when the normality tests examined in all distributions were taken into account and compared, it was concluded that the Shapiro-Wilk gives better results than other tests in general for normal and non-normal distributions, and that D'Agostino -Pearson, Skewness and Jargue-Bera tests were also stronger than the other tests. In addition, it was determined that the increase in sample sizes increased power of the test. In conclusion, it can be said that in addition to the distribution pattern, type-I error probability and sample size are also very important factors for test power.