In this study, Shapiro-Wilks, Lilliefors and Kolmogorov-Smirnov tests were compared for Type I error and for power of the tests. The simulation was run 100, 000 times for different situations and for different types of departures from normality. For all different sample sizes and distributions, Shapiro-Wilks gave the most powerful results, followed by the Lilliefors test. Kolmogorov-Smirnov test results were the weakest among all three tests. All three test were most powerful when ran on data with exponential distribution.