Normality Assessment, a Substantial Appraisal in Medical Studies: A Simulation Study for Power Comparison of Various Types of Normality Tests

Background: In medical research, statistical tests have become more important. Several parametric procedures are available but each of them requires normality assumption. As normality violation may affect interpretation and inferences reliability and validity, so importance of normal distribution is undeniable. Although several normality tests available for software users but the power of each test in specified situation is not clear.
Methods: The aim of this study is to compare the power of nine normality tests. In this paper power of Jarque-Bera test, D’Agostino and Pearson test, Chi-square test, Kolmogrov-Smirnov test, Lilliefors test, Cramer-Von Mises test, Anderson-Darling test, Shapiro-Wilk test and Shapiro-Francia test compared via Monte Carlo simulation of sample data generated from alternative distributions that follow symmetric, skewed, skewed & heavy tailed, highly skewed and highly skewed & heavy tailed distributions.
Results: Simulation study shows that Shapiro-Francia test under symmetric, skewed, skewed& heavy tailed and highly skewed& heavy tailed distributions perform better than others. Also, Shapiro-Wilk performs better when underlying distribution is skewed.
Conclusion: Although, Shapiro-Francia and Shapiro-Wilk have greater power than their competitors but their powers are still low for small sample size. So their singly use is not recommended.