Preliminary Tests of Homogeneity - Type I Error Rates under Non-Normality

Abstract

Many statistical procedures utilize preliminary tests to enhance the accuracy of the final inferences. Preliminary tests like Goldfeld-Quandt (GQ) and Levene-type tests are used to assess the assumption of equality of population variances with normality as the underlying distributional assumption. Such tests must be used with care as the final inferences are conditional on the performance of these tests at first stage. This study explores the size distortions of GQ and Levene-type tests under non-normality. The results do not warrant the use of GQ & Levene test under non-normality as the size distortions are as high as 88 & 48% for the respective statistics. However, the modified form of Levene test (BF-test) retains its size properties except for the multi-model alternatives with relatively big outliers.