STATISTICAL METHODS IN MEDICAL RESEARCH II. SAMPLE SIZES REQUIRED IN EXPERIMENTS INVOLVING ALL-OR-NONE RESPONSES

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Abstract
In order to obtain a reliable estimate of the sample size (number of individuals) required in an experiment, an investigator must first specify: (1) what risk he is willing to run of mistakenly concluding that his different experimental treatments have produced different effects; (2) what the magnitude of the effect produced by one of the treatments is likely to be; (3) what magnitude of difference between treatment effects would be important to him; (4) what risk he is willing to run of failing to detect a difference when it is of that magnitude—the risk of an unsuccessful experiment. Difficulties in answering these questions are discussed with reference to five examples from different types of medical research. For experiments involving the comparison of two treatments that produce an all-or-none effect such as death or survival, a table derived from binomial expansions is presented, which, for samples containing up to 100 individuals, shows the probabilities of successful experiments for different magnitudes of treatment effects.

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