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Biometrika 1988 75(2):207-214; doi:10.1093/biomet/75.2.207
© 1988 by Biometrika Trust
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Robustness and power of tests for a null variance ratio

PETER WESTFALL

College of Business Administration, Information Systems and Quantitative Sciences, Texas Tech University Lubbock, Texas 79409, U.S.A.

A locally optimal test for a null variance ratio is considered in the context of the one-way random effects model, when normality is assumed. Using an asymptotic design sequence with an increasing number of groups with bounded but unequal sizes, this test has the correct asymptotic level of significance for nonnormal data, a property which is not shared by the competing Wald test. Asymptotic power calculations demonstrate that the locally optimal test may be more powerful than the Wald test even in situations where the actual significance level of the Wald test overstates the nominal level.

Key Words: Asymptotic normality • Invariance • Pitman alternative • Random effects • Unbalanced design


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