A Power Comparison of Goodness-of-fit Tests for Normality Based on the Likelihood Ratio and the Non-likelihood Ratio

The goal of the study is to select the best goodness-of-fit test among six tests; the Z(A) statistic, the Z(C) statistic, the Z(K) statistic, the Anderson-Darling (A(2)) statistic, the Shapiro-Wilk (W) statistic and the Shapiro-Francia statistic (W '). The tests were compared when the normal parameters are unknown and sample sizes are 10, 30, 50, 70 and 100 each with 0.05 level of significance. With 1,000 Monte Carlo replications, the probability of type I error of all six statistics can be controlled for all sample sizes under study. Both sample sizes and types of the distribution affect the power of the test.