On small-sample confidence intervals for parameters in discrete distributions

Biometrics. 2001 Sep;57(3):963-71. doi: 10.1111/j.0006-341x.2001.00963.x.


The traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level. In constructing such intervals for parameters in discrete distributions, less conservative behavior results from inverting a single two-sided test than inverting two separate one-sided tests of half the nominal level each. We illustrate for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio.

Publication types

  • Comparative Study
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Biometry*
  • Confidence Intervals*
  • Likelihood Functions
  • Odds Ratio
  • Proportional Hazards Models
  • Sampling Studies
  • Statistical Distributions