A Targeted Investigation into Clopper-Pearson Confidence Intervals

William C.L. Stewart, Susan E. Hodge


In this special report, we consider Clopper-Pearson (CP) confidence intervals (CIs) for the binomial probability distribution. We review their direct construction from coverage probabilities, and review how this construction corresponds to the more common derivation based on hypothesis testing. We then explore some features of CP CIs: We use the direct construction to elucidate their bizarre patterns of coverage and to understand the origin of these patterns. We present an argument for constructing closed rather than open CIs; and we show how poorly the uncorrected normal approximation performs relative to CP CIs, even when n is large (e.g., n = 500). We briefly discuss the difference between CP and fiducial CIs. These insights should provide users with a different perspective on and appreciation of Clopper-Pearson CIs.


confidence intervals, Clopper-Pearson, fiducial intervals, and coverage

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DOI: http://dx.doi.org/10.18103/imr.v4i4.655


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