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estimation of confidence intervals (CIs) of binomialproportions has been reviewed more than once but the directionalinterpretation, distinguishing the overestimation from the underestimation, wasneglected while the sample size and theoretical proportion variances fromexperiment to experiment have not been formally taken in account. Herein, wedefine and apply new evaluation criteria, then give recommendations for thepractical use of these CIs.  Materials & methods: Google Scholar was used for bibliographic research.Evaluation criteria were (i) one-sided conditional errors, (ii) one-sided localaverage errors assuming a random theoretical proportion and (iii) expectedhalf-widths of CIs.  Results: Wald's CI did not control any of the risks, even when the expectednumber of successes reached 32. The likelihood ratio CI had a better balancethan the logistic Wald CI. The Clopper-Pearson mid-P CI controlled wellone-sided local average errors whereas the simple Clopper-Pearson CI wasstrictly conservative on both one-sided conditional errors. The percentile andbasic bootstrap CIs had the same bias order as Wald's CI whereas thestudentized CIs and BCa, modified for discrete bootstrap distributions, wereless biased but not as efficient as the parametric methods. The half-widths ofCIs mirrored local average errors.  Conclusion: we recommend using the Clopper-Pearson mid-P CI for theestimation of a proportion except for observed-theoretical proportioncomparison under controlled experimental conditions in which theClopper-Pearson CI may be better.

Two-sided confidence interval of a binomial proportion: how to choose?