A note on the rubustness of the lilliefors test for univariate normality with respect to equicorrelated data

Abstract

The Lilliefors test, which was developed by Lilliefors (1967), is a well-known test for univariate normality when population parameters are unknown. The main assumption for implementing the test is the independent-data assumption. This paper demonstrates the robustness of the Lilliefors test against equicorrelated observations. More specifically, we show that the null distribution of the Lilliefors test statistic is invariant under the alternate assumption that the observations are equicorrelated.