A modified Lilliefors normality test

A test statistic was proposed with the intent of modifying Lilliefors Test for normality. Rather than considering only the largest difference between the Cumulative Standard Normal Distribution Function (Cumulative Distribution Function) and the Empirical Distribution Function (Empirical Distribution Function); the proposed statistic uses the sum of all differences between the Cumulative Distribution Function and Empirical Distribution Function. The desired result was to increase the power of the test by incorporating more information with very little increase in computation difficulties. The proposed test was compared directly to Lilliefors Test, the Anderson-Darling Test, and the Shapiro-Wilkes Test in terms of significance and power for similar sample sizes and alpha levels.;Results showed that the proposed test statistic had similar accuracy in regards to significance levels when compared to the other tests. Accuracy of the significance level was a concern due to the critical values being simulated rather than based on theoretical distributions. Simulation has no more inherent error than does the asymptotic nature of sampling distributions.;The power analysis itself revealed an increase in power across every sample size and significance level for each of fourteen alternative distributions. The method employed showed a clear improvement in terms of power over the original Lilliefors test. When compared to the Shapiro Wilk Test, arguably the most powerful widely used test available, the proposed test generally came up short. The only exceptions were for data from a Laplace distribution (having extreme observations in both tails) and for distributions with less kurtosis than a Normal distribution in the case of both small sample sizes and high significance levels.;The methodology employed in the study showed an increase in performance over the original method. It is reasonable then to employ a similar method for any test or procedure which considers only the maximum distance between two functions. Specifically the Kolmogorov Smirnov Test could be improved in this fashion; a directly useful test would result. Another improvement would be to combine these findings with another modification of the Kolmogorov Smirnov Test, allowing it to test discrete data. Together these modifications could demonstrate superior power to the ÷² goodness-of-fit test with the same level of flexibility.