GENERALIZED F-TESTS FOR UNBALANCED NESTED DESIGNS UNDER HETEROSCEDASTICITY

Two-factor fixed-effect unbalanced nested design model without the ass umption of equal error variance is considered. Using the generalized d efinition of p-values, exact tests under heteroscedasticity are derive d for testing ''main effects'' of both factors. These generalized F-te sts 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 a re briefly discussed.