Generalized F-tests for unbalanced nested designs under heteroscedasticity

Two-factor fixed-effect unbalanced nested design model without the assumption of equal error variance is considered. Using the generalized definition of p-values, exact tests under heteroscedasticity are derived for testing ''main effects'' of both factors. These generalized F-tests can be utilized in significance testing or in fixed level testing under the Neyman-Pearson theory. Two examples are given to illustrate the proposed test and to demonstrate its advantages over the classical F-test. Extensions of the procedure for three-factor nested designs are briefly discussed.