A Modified Lilliefors Normality Test

• Activity Number: 548
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Benjamin Overholt*+ and Jay Schaffer
• Companies: and University of Northern Colorado
• Keywords: Normality ; power ; lilliefors ; Kolmogorov

Abstract

Overholt, Benjamin A. and Jay Schaffer A Modified of Lilliefors Normality Test. Published Doctor of Philosophy dissertation, University of Northern Colorado, 2013. 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 (CDF) and the Empirical Distribution Function (EDF); the proposed statistic uses the sum of all differences between the CDF and EDF. The desired result was to increase the power of the test by incorporating more information with very little increase in computational 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. The power analysis itself revealed an increase in power across every sample size and significance level for each of fourteen alternative distributions when compared to Lilliefors test, and rivaled the power of the other tests used with little increase in test complexity.