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Biometrika 1990 77(4):797-805; doi:10.1093/biomet/77.4.797
© 1990 by Biometrika Trust
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Locally optimal design for comparing two probabilities from binomial data subject to misclassification

HERMAN CHERNOFF and YOEL HAITOVSKY

Department of Statistics, Harvard University Cambridge, Massachusetts 02138, U.S.A.
Departments of Economics and Statistics, Hebrew University Jerusalem 91905, Israel

Optimal experimental designs are found for estimating the difference P1–P2 of two population probabilities, using measuring instruments possibly subject to known error rates. The available experiments considered are to measure, for i = 1 or 2, the outcome of a trial on the population i without error, or with error, or with error with the possibility of checking either positive or negative responses. Given that the cost per observation depends on which experiment is carried out, an asymptotically locally optimal allocation is derived in terms of results of Elfving which provide a simple geometrical solution which is easily generalized.

Key Words: Asymptotic relative efficiency • Classification error • Conditional resampling • Double sampling • Equality between two success probabilities • Hypothesis testing • Optimal experimental design


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