Comparison of General Linear Model Approaches to Testing Variance Heterogeneity in True and Quasi-Experiments

Abstract

Simulation results indicated that when groups were sampled from the same platykurtic population the O'Brien (1981) transformation was preferred except when a positive sample size/variance correlation existed, then the Welch test performed on the O'Brien scores was more powerful. Also consistent with previous research, when grouped data were sampled from the same leptokurtic population the Brown & Forsythe (1974) transformation was preferred for equal sample sizes. The O'Brien test was more powerful with an indirect sample size/variance relationship regardless of distribution shape (e.g., Algina et al., 1989; Olejnik & Algina, 1987, 1988). The study also demonstrated that the Welch test performed on Brown-Forsythe scores was more powerful when a positive sample size/variance correlation existed in leptokurtic data. Furthermore, choosing a test of variance based on an initial test of kurtosis may improve power (Ramsey, 1994). When data were sampled from populations with drastically different shapes (kurtosis), the Type I error rate of most tests was unstable excluding the Hartley Fmax test which performed surprisingly well.