  Introduction: estimation of confidence intervals (CIs) of binomial
proportions has been reviewed more than once but the directional
interpretation, distinguishing the overestimation from the underestimation, was
neglected while the sample size and theoretical proportion variances from
experiment to experiment have not been formally taken in account. Herein, we
define and apply new evaluation criteria, then give recommendations for the
practical use of these CIs.
  Materials & methods: Google Scholar was used for bibliographic research.
Evaluation criteria were (i) one-sided conditional errors, (ii) one-sided local
average errors assuming a random theoretical proportion and (iii) expected
half-widths of CIs.
  Results: Wald's CI did not control any of the risks, even when the expected
number of successes reached 32. The likelihood ratio CI had a better balance
than the logistic Wald CI. The Clopper-Pearson mid-P CI controlled well
one-sided local average errors whereas the simple Clopper-Pearson CI was
strictly conservative on both one-sided conditional errors. The percentile and
basic bootstrap CIs had the same bias order as Wald's CI whereas the
studentized CIs and BCa, modified for discrete bootstrap distributions, were
less biased but not as efficient as the parametric methods. The half-widths of
CIs mirrored local average errors.
  Conclusion: we recommend using the Clopper-Pearson mid-P CI for the
estimation of a proportion except for observed-theoretical proportion
comparison under controlled experimental conditions in which the
Clopper-Pearson CI may be better.

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