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Biometrika 1969 56(3):553-560; doi:10.1093/biomet/56.3.553
© 1969 by Biometrika Trust
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The use of random allocation for the control of selection bias

STEPHEN M. STIGLER

University of Wisconsin Madison

In comparing two treatments, suppose the suitable subjects arrive sequentially and must be treated at once. In such situations, if the experiment calls for fixed treatment numbers, the experimenter can, using his knowledge of the number of treatments that have been assigned, bias the experiment by his selection of subjects. If we consider the method of assigning treatments as an experimental design, Blackwell & Hodges (1957) have shown that the minimax design is the truncated binomial. In this paper we show that random allocation is a restricted Bayes design within the class of Markov designs, and is in many senses preferable to the minimax design. In particular, it is possible for the random allocation design effectively to eliminate the bias asymptotically when the minimax design does not, and in no case will random allocation have a much worse performance than the minimax.


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S. M. Stigler
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