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Biometrika 1987 74(4):863-870; doi:10.1093/biomet/74.4.863
© 1987 by Biometrika Trust
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Approximations to the power of some order restricted tests with slippage alternatives

BAHADUR SINGH and F. T. WRIGHT

Department of Mathematical Sciences, Memphis State University Memphis, Tennessee 38152, U.S.A.
Department of Mathematics and Statistics, University of Missouri-Rolla Rolla, Missouri 65401, U.S.A.

In the one-way analysis of variance, a researcher may believe that the ordering of the means is known and would like to incorporate this information into the test of hypotheses. Bartholomew developed likelihood ratio tests for such situations and proposed a two-moment chi-squared approximation for the minimum power of the test for the case of known variances. The accuracy of a closely related approximation is studied and an approximation based on mixtures of noncentral F variables is developed for the case of unknown variances. The simple ordering, the simple tree ordering and a class of slippage alternatives are considered, and an example concerning the choice of sample size needed to provide a specified power at a particular alternative is treated. For powers in the range typically of interest the two-moment approximation seems adequate.

Key Words: Approximation to power • Order restricted test • Simple order • Simple tree ordering • Slippage alternative


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