Binomial Distributed Data Confidence Interval Calculation: Formulas, Algorithms and Examples

When collecting experimental data, the observable may be dichotomous. Sampling (eventually with replacement) thus emulates a Bernoulli trial leading to a binomial proportion. Because the binomial distribution is discrete, the analytical evaluation of the exact confidence interval of the sampled outcome is a mathematical challenge. This paper proposes three alternative confidence interval calculation methods that are characterized and exemplified.

Automated summary

This paper discusses the challenge of mathematically evaluating the exact confidence interval for sampled outcomes, which follow a binomial distribution. It proposes three alternative methods for calculating confidence intervals and provides descriptions and examples for each.