A Distribution Free Test for the Equality of Scales

Abstract

Situations where scale parameters are not nuisance factors to be controlled but outcomes to be explained arise in many contexts such as quality control, agricultural production systems, experimental education, the pharmaceutical industry and biology. Tests for homogeneity of variances are often of interest also as a preliminary to analysis of variance, dose-response modelling or discriminant analysis. The literature on tests for the equality of scales is vast. A test which usually stands out in terms of power and robustness against non normality is the modified Levene W50 test, however in the literature no test is found to be the most powerful one for every distribution. The goal of the article is to propose an effective method for comparing scales. More precisely, we propose a test for the equality of scales that, even though was not the most powerful one for every distribution, it has good overall performance under every type of distribution. This test has the form of a combined resampling test. It is important to note that non combined tests show good performance only in particular contexts. Size and power of the proposed test are studied via simulation and compared with many other robust tests for scale. A practical application to industrial quality control is discussed.

Keywords:

• Combined tests
• Distribution-free scale testing
• Robustness

Mathematics Subject Classification:

• 62G09
• 62G10
• 62G35