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Confidence intervals for a binomial proportion

S E Vollset1

  • 1Section for Medical Informatics and Statistics, University of Bergen, Haukeland Hospital, Norway.

Statistics in Medicine
|May 15, 1993
PubMed
Summary
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The standard textbook method for binomial confidence intervals is unreliable. The continuity corrected score method offers superior accuracy and is recommended for all sample sizes.

Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Methods

Background:

  • Binomial confidence intervals are crucial for estimating population proportions from sample data.
  • Existing methods for calculating these intervals vary in accuracy and applicability.
  • The standard textbook method and common rules of thumb often lead to inadequate precision.

Purpose of the Study:

  • To compare thirteen different methods for computing binomial confidence intervals.
  • To evaluate methods based on coverage properties, interval widths, and accuracy relative to exact limits.
  • To identify the most reliable method for constructing binomial confidence intervals.

Main Methods:

  • Comparative analysis of thirteen distinct binomial confidence interval calculation methods.

Related Experiment Videos

  • Evaluation of coverage functions, interval widths, and errors against exact limits.
  • Assessment of score limits derived from quadratic equations and continuity correction.

    • Main Results:

    • The standard textbook method (x/n +/- 1.96 sqrt[(x/n)(1-x/n)/n]) and its continuity corrected version are strongly discouraged.
    • A common rule of thumb (np > 5 and n(1-p) > 5) does not guarantee sufficient accuracy.
    • Score limits, particularly the continuity corrected version, demonstrate superior performance.
    • The continuity corrected score method is recommended over exact methods due to its coverage properties.

    Conclusions:

    • The continuity corrected score method is the recommended approach for calculating binomial confidence intervals.
    • Users should be aware of the conservative nature of the continuity corrected score method.
    • Omission of continuity correction can lead to wider fluctuations in actual coverage, impacting reliability.