Distribution-Free Tests for One-Way Homoscedasticity in a Two-Way Classification

Abstract

Homoscedasticity is an important assumption for the analysis of variance of data from a two-way table. A preliminary test for equality of row (column) variances is often in order. Moreover, the row (column) variance may be a parameter characterizing physical or biological properties of the treatment associated with a row (column), e.g., in the analysis of measurement errors or in the analysis of phenotypic stability. In this case, a test for homoscedasticity is central to the statistical analysis. Unfortunately, parametric procedures available for this problem are quite sensitive to the underlying assumption of normality. This paper examines two rank tests given by Nassar and Hiihn (1987, Biometrics 43, 45-53) and Hiihn and Nassar (1989, Biometrics 45, 977-1000), which are applicable for detecting homoscedasticity in a two-way classification. These tests are approximately valid for normally distributed errors, but they may be anticonservative for nonnormal distributions. A modification is suggested that leads to a distribution-free test for homoscedasticity in a two-way layout. Simulations indicate that under normality the modified test has low power compared to parametric tests.