The assessment of normality tests for studies with large sample sizes

In order to reach distinct statistical inferences, it is required to verify that several case-specific assumptions on data are satisfied. One of the most important among these different assumptions is the normality assumption; indeed, many parametric tests such as correlation, regression, t tests and variance analysis depend on this assumption. It is for that reason that researchers will be able to make strong inferences with parametric analyses when the data has normal distribution.In this study, our main aim is to provide comparisions of strengths and weaknesses of commonly used normality tests under various conditions based on the fact that in large samples even minor deviations from normality can still be statistically significant. Our study is based on different statistical approaches observed during searches by scanning PubMed and Google Scholar which are used widely by researchers and chosen among the normality tests which are included in statistical package programs. The performances of tests are assessed under various conditions. For these assesments, data with distinct sizes and properties are produced by the R program. We conclude that the assessments of type 1 error rates of the Pearson's chi-squared, Kolmogorov-Smirnov, Lilliefors, Anderson-Darling, D'Agostino's K-Squared, Jarque-Bera, Shapiro-Wilk, Shapiro-Francia, Cramer-Von Mises normality tests are similar for the purpose of comparisons of the powers of methods. When aforementioned normality tests are applied to data obtained by removing a certain part of the data which is produced from normal distribution and to data obtained by different distributions, Shapiro-Wilk, Shapiro-Francia tests are leading in power. For data produced by using various skewness and kurtosis values the strongest results are obtained by the D'Agostino's K-Squared test. Keywords: large samples, skewness and kurtosis, normality tests, the power of test, type 1 error