On approximating probability distributions of a statistic of brown-forsythe from normal and non-normal universes

Abstract

This article considers a one-way ANOVA model as given in (1.1) with heterogeneous variances. The distributions of the Brown-Forsythe F * statistic for this model are derived and approximated by Laguerre polynomial expansions. The Type 1 error and power function values are then evaluated for both normal and mixtures of two normals populations. For the example with k=3n 1=8,n 2=10 and n 3=12. it is shown that the Satterthwaite approximation provides a close approximation to the null and non-null distributions in most o the cases. It is shown that the F * is quite robust with respect to departure from normality for Type 1 error in the case of mixtures of two normals.