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Biometrika 1987 74(4):687-694; doi:10.1093/biomet/74.4.687
© 1987 by Biometrika Trust
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Precision of double sampling estimators for comparing two probabilities

JUNI PALMGREN

National Public Health Institute Kalliolinnantie 4, 00140 Helsinki, Finland

It is assumed that both error-prone and error-free observations can be made on a binary response, the second type being more expensive. In double sampling error-prone observations are made on all sample units and for a random subsample error-free observations are made as well. Tenenbein (1970) studied allocation of units in double sampling for estimating a single probability. We consider double sampling for comparing two probabilities. For different cost ratios for error-prone versus error-free observations and for fixed total cost, we assess how the large-sample variance of the log odds ratio estimator varies with the proportion of units subject to both error-prone and error-free observation. We determine the optimal double sampling proportion and the possible gain from using double sampling versus single sampling in which only error-free observations are made.

Key Words: Binary data • Double sampling • Misclassification • Odds ratio • Optimal allocation


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