UNBALANCED TWO-WAY ANOVA ADDITIVE MODEL UNDER HETEROSCEDASTICITY USING GENERALIZED p-VALUES

Two-factor fixed-effect unbalanced additive model without the assumption of equal variances is considered. By taking the generalized p-value approach, the classical F-test for the main effects of the unbalanced additive model is extended to the case of unequal error variances. This generalized F-test can be utilized in significance testing or in fixed level testing under the Neyman-Pearson theory. This nontrivial extension is similar to the generalized F-test for the two-way ANOVA model under heteroscedasticity. Examples are cited to illustrate the proposed test and to demonstrate the significance and verification of this new model that are worthwhile to resort to a numerically extensive testing procedure when the problem of heteroscedasticity is serious or the assumption of homoscedasticity is not reasonable in additive models.