Friday, 11 December 2009

Testing Homogeneity of Variance

This series of posts aims to compare empirical type I error and power of different tests that have been proposed to assess the homogeneity of within-group variances. The main questions answered in the following posts (based on a recent project with University of Newcastle) are:

(1) Which tests are most effective (powerful and robust) when testing the homogeneity of variances in various conditions of heterogeneity, and

(2) When these conditions exist, do any of the tests of homogeneity of variance prove more effective in the detection of heterogeneity than others?

An introductory simulation study was conducted that established that Anova is extremely susceptible to heterogeneity of the variances. This occurs both in normally distributed and non-normal datasets. Even small deviances from homogeneity to that of heteroscedasticity results in inflated type I error.

A subsequent simulation study was conducted. The purpose of this study was to determine which of the tests of homogeneity of variances preformed best in unfavourable conditions. These conditions included small sample sizes and a number of non-normal distributions. In these conditions, Bartlett's or Box's tests perform well. Conversely, Cochran's test and the Log Anova test exhibited low power with small to moderate sample sizes even with normally distributed datasets. A decision tree has been created for these results that can be used to determine the most effective test strategy.

Keywords: Anova; Wald, Levene, permutation test; power; simulation study; test of homogeneity of variances; t-test; type I error, robust.

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