Report a Proportion with a Wilson Confidence Interval

Define the event and eligible denominator

Begin with a binary outcome, a population, and a measurement window. Write what counts as an event and which observations belong in the denominator. Twenty events among one hundred observed participants is not automatically the same quantity as twenty events among everyone originally enrolled.

Confirm that the observations fit an independent binomial model. Repeated visits, clustered participants, survey weighting, or censoring can require a different uncertainty calculation. A proportion calculator cannot determine whether those features are present from two entered numbers.

Name the interval method

The sample proportion is events divided by observations. Several methods can place an interval around it, and their limits need not agree. The official statsmodels proportion-interval documentation identifies Wilson as a score-based interval option alongside other methods.

Record the confidence level and method in the analysis specification. Do not switch methods after seeing which interval avoids an inconvenient boundary. Wilson limits are not obtained merely by attaching the usual symmetric normal margin to the observed proportion, and they need not be symmetric around it.

Check fictional counts

Suppose 20 of 100 independent observations meet the event definition. The observed proportion is 20%. A two-sided 95% Wilson interval is approximately 13.34% to 28.88%. The Wilson-proportion tool can reproduce these invented counts.

Now consider zero events in 20 observations. The observed proportion is zero, but the 95% Wilson interval extends from zero to approximately 16.11%. Observing no events does not establish that the population probability is exactly zero. These examples illustrate uncertainty calculations, not evidence about any real intervention or disease.

Preserve the denominator audit

Use the proportion interval worksheet to record event criteria, counts, confidence level, method, source, and exclusions. Check that events are whole nonnegative counts and do not exceed the total. A percentage alone may not provide enough information to recover the original counts after rounding.

Report both the numerator and denominator beside the estimate and interval. Explain missing-outcome handling rather than silently classifying unknown outcomes as non-events. For multiple related proportions, consider whether the reporting plan involves multiplicity or a different estimand; a collection of separate intervals does not automatically provide simultaneous coverage.

Interpret confidence as a property of the interval procedure under its assumptions, not as a probability assigned to the fixed parameter by this frequentist calculation. Finish with the observed result, explicit uncertainty method, and the population to which the statement applies. A bounded, plausible-looking interval cannot compensate for selection bias, measurement error, or an incorrectly chosen denominator.

Source checked on 3 November 2026; fictional intervals independently recalculated.