GENERALIZED F -TESTS FOR UNBALANCED NESTED DESIGNS UNDER HETEROSCEDASTICITY

MALWANE M. A. ANANDA

Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154, U.S.A.

(Received November 4, 1994; revised April 10, 1995)

Abstract. 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 threefactor nested designs are briefly discussed.

Key words and phrases: Nested design, unbalanced models, heteroscedasticity, generalized p-values.