Testing for Main Random Effects in Two-Way Random and Mixed Effects Models: Modifying the F Statistic

A procedure for testing the significance of the main random effect is proposed under a model which does not require the traditional assumptions of symmetry, homoscedasticity, and normality for the error term and random effects. To accommodate this level of model generality, and also unbalanced designs, suitable adjustments to the F-test are made. The extensive simulations performed under the random effects model, and the unrestricted and restricted versions of the mixed effects model, indicate that the classical F procedure is extremely liberal under heteroscedasticity and unbalancedness. The proposed test procedure performs well in all settings and is comparable to the classical F-test when the classical assumptions are met. An analysis of a dataset from the Mussel Watch Project is presented.