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I've always used a Clopper-Pearson interval for binomial confidence intervals, but never questioned why (it's the default in ROOT). I found http://en.wikipedia.
by cozzyd 12y ago
I've always used a Clopper-Pearson interval for binomial confidence intervals, but never questioned why (it's the default in ROOT). I found http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval http://en.wikipedia.org/wiki/Binomial_proportion_confidence_... quite useful. Sounds like using Clopper-Pearson is safer than using a Wilson interval .
- louden 12y agoIt's a trade off. Clopper-Pearson can be overly conservative in many instances. I tend to use Jeffreys interval personally, which is a Bayesian method. Brown et al. give a formal treatment of the subject with simulations showing actual coverage probabilities for the various methods. It is worth a read if you want to really dive into the subject. ref: Brown, Lawrence D.; Cai, T. Tony; DasGupta, Anirban (2001). "Interval Estimation for a Binomial Proportion". Statistical Science 16 (2): 101–133
- cozzyd 12y agoThanks. To save others the trouble, a (apparently accessible to all?) link to that article is at http://projecteuclid.org/download/pdf_1/euclid.ss/1009213286 http://projecteuclid.org/download/pdf_1/euclid.ss/1009213286 It looks like Clopper-Pearson is the only method guaranteed to not underestimate the size of the confidence interval (which makes sense, given its derivation), but it almost always overestimate its (unless your confidence interval exactly matches the discrete p-values allowed by the binomial distribution).