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The Rule of Three states that 3/n is an upper 95% confidence bound for binomial probability p when in n independent trials no events occur. We discuss the derivation of this rule, its validity in small samples, and propose some alternatives. The material may serve well as a thought-provoking introduction to a clinical trials, statistical consulting, or a categorical data class, and is interesting on its own merit.
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Jovanovic et al. (1997) studied this question.
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