Assessing Homoscedasticity Graphically

Abstract

The problem of homoscedasticity arises in several fields such as business, education, environments, and medicine, and common question in many statistical analyses. One of the most important tests in this direction is Levene test and its robust version Brown-Forsythe test. The goal of this paper is threefold. The first goal is to propose an expression that enable to develop a graphical way for Levene-Brown-Forsythe tests. The second goal is to derive the sampling distribution of the proposed expression as the generalized beta prime distribution. The third goal is to provide deep insight and understanding where the dispersion effects occur. Simulation study is carried out to study the level of significance and power of the proposed test in comparison with the original Levene-Brown-Forsythe tests. The results are of great values since the proposed method provides (a) powerful visual tool and deep insight for testing homoscedasticity, (b) keeps the size and power of the test similar to Levene-Brown-Forsythe tests, and (c) does not need to pairwise comparisons. Two applications are presented to show the utilities of the proposed method.

Keywords

• Beta distribution
• Bonferroni approximation
• homogeneity of variance
• nonnormality
• test power
• type I error