Some multiple comparison procedures for variances from non-normal populations
Comparative tests of variances are of interest to both statisticians and scientists. Traditional parametric methods often require unrealistic assumptions about the characteristics of the data, the most common of which is that the data are normally distributed. While non-parametric methods release the analyst from many of these assumptions, this is typically at the expense of the power of the test. We discuss existing techniques and present new methods, which are powerful and robust to non-normality, for performing multiple comparisons of variances. We investigate several tests for homogeneity of variance and use variations of them to demonstrate our multiple comparisons procedures. Our research concentrates on those procedures which focus on the population variances, although we consider procedures based on deviations from location measures due to their demonstrated power. First, we introduce and expand upon the utilization of bootstrap methods for the purpose of variance testing. Then, we leverage developments in improved Bonferroni techniques and adjusted p-values to further refine our procedures. The methods presented herein are applicable in the all possible pairwise comparisons and treatment versus control hypothesis testing scenarios. Our procedures may also be used to perform the homogeneity of variances test.
multiple comparisons of variances bootstrap adjusted p-values corrected p-values modified bonferroni