Comparison of Semiparametric Approaches to Two-Way ANOVA in the Presence of Heteroscedasticity

Factorial analysis of variance designs is commonly used in several fields like biology, ecology and social sciences. However, in practice, the underlying assumptions, normality and homoscedasticity, are easily violated. In recent years, several alternative tests were proposed to relax these assumptions, the Wald-type statistics and the ANOVA-type statistics, and tests based on the permutation of observations. Few studies are focusing on the performance of the permutation tests in the presence of heterogeneity. This work intends to contribute to this last analysis. A simulation study is carried out, considering balanced designs, with an equal number of factor levels and several types of discrete distributions with different degrees of dispersion.