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GENERALIZED *F*-TESTS FOR UNBALANCED NESTED DESIGNS

UNDER HETEROSCEDASTICITY

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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 three-factor nested designs are briefly discussed.

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

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