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

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