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Abstract:
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In some disciplines (e.g., experimental biology; ecology), it is of scientific interest to investigate whether the variability of an outcome is affected by an experimental treatment or changes over time (e.g., with age). Several tests for differences in variances in basic between-subjects designs have been developed. These procedures transform the original response, y, then perform one-way ANOVA on the transformed data. The Levene (1960) approach of performing ANOVA on the squared residuals (e2) was generalized to linear regression models by Breusch and Pagan (1979). Variance Function Regression (VFR) uses a generalized linear model with the squared residuals (e2) as the response, a log link function, and a gamma distribution to account to the right-skewed nature of e2. A simulation study will investigate how these methods for testing variances perform in terms of test size and power for three models: between-subjects ANOVA, repeated measures, and general regression. Three distributions (normal, skewed, symmetric-heavy-tailed) for the linear model residuals will be investigated.
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