New Methods using Levene Type Tests for Hypotheses about Dispersion Differences

Abstract

Testing equality of scale arises in many research areas including clinical data analysis. In contrast to procedures for tests on means, tests for variances derived assuming normality of the parent populations are highly non-robust to non-normality. Levene type tests are well known to be robust tests for equality of scale for the one-way design; the current standard test uses the ANOVA F test on absolute deviations from the sample medians. We first develop a new modified version of the standard Levene test that improves its null performance and power. Applying the Box-Anderson correction to the ANOVA F test further improves the performance.

We also extend the robust Levene type tests to the two-way design with one observation per cell, the randomized complete block design (RCB). Currently, the available Levene type tests for RCB designs employ either standard ANOVA F tests on the absolute values of ordinary least squares (OLS) residuals, or weighted least squares (WLS) ANOVA F tests on the OLS residuals. These two tests can be liberal, especially under non-normal distributions. Instead, we use OLS ANOVA F tests on the absolute values of residuals obtained from models fit by least absolute deviation (LAD) estimation and by Huber Proposal 2 M-estimation. We also apply bootstrap methods to these Levene type tests and compare by simulation these Levene type tests in terms of robustness and power.