Power Comparisons of Shapiro-Wilk, Kolmogorov-Smirnov and Jarque-Bera Tests

The importance of normal distribution is undeniable since it is an underlying assumption of many statistical procedures. When the normality assumption is violated, interpretation and inferences may not be reliable or valid. This paper compares the power of three formal tests of normality: Shapiro–Wilk test, Kolmogorov–Smirnov and Jarque–Bera test. Power comparisons of these three tests were obtained via Monte Carlo simulation. Critical values were obtained for each normality test statistic for sample sizes: n1 = 20, n2 = 50, n3 = 100, n4 = 200, n5 = 300, n6 = 400, n7 = 500 and n8 =1000. The critical values were obtained based on 10,000 simulated samples from a normal distribution. Results show that Shapiro–Wilk test is the most powerful normality test, followed by Jarque–Bera test and Kolmogorov–Smirnov test.

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