Robust tests for two-way ANOVA models under heteroscedasticity

Abstract

The aim of this research was to compare the robustness of two heteroscedastic test statistics, the Welch-James statistic developed by Johansen (WJ) and the Type-Box statistic developed by Brunner, Dette and Munk (BDM), together with the General Linear Model (GLM), not heteroscedastic test statistic, in two different manners depending on the calculation of the critical value. On the one hand, when the critical values are based on theoretical values (WJ, BDM and GLM respectively), and on the other hand, when they are obtained by means of bootstrap resampling (WJB, BDMB and GLMB respectively). To carry out it a study of simulation was realized on a factorial design lacking in homogeneity, normality and orthogonally. The results show that when the relation between the size of the cells and the size of the variances was positive the procedure WJ was the most robust and that when the relation was negative the most robust procedure was WJB. Both procedures behaved in a liberal way when the shape of the distribution was skewed, in major measure major it were the degree of inequality of the size of the cells and the heterogeneity of the variances.