Type 1 Error Rate of Some Normality Tests

Most Statistical procedures require normality of data for a reasonable interpretation and inference. Failure of this assumption invariably undermines the applicability of such data. Using a statistical method that requires normality of the data when the data is not normal will lead to misleading inference. Quite a number of procedures exist in literature in verifying the normality assumption. This paper examines simulated 10,000 normally distributed data and assessed them for normality using Anderson-Darling test (AD-test), Kolmogorov-Smirnov test (KS-test) and Shapiro-Wilk test (SW-test). The results of the analysis show that AD-test outperforms the other two tests. However, for sample size 20 or less, KS-test outperforms the rest. The sum of ranks of type 1 error rate showed that the AD-test is the best because it has the lowest rank sum. It is followed by the KS-test and the SW- test has the largest sum of ranks and hence the poorest. The type 1 error rate of each test does not show any consistent pattern as the sample size increases. Hence, it can be inferred that sample size does not have significant impact on the type I error of a test.