Formula and example
How it is calculated
With p=k/n: centre=(p+z²/(2n))/(1+z²/n); half-width=z·√[p(1−p)/n+z²/(4n²)]/(1+z²/n).
Worked example
50 successes in 100 independent observations give 50%. The 95% Wilson interval runs from approximately 40.38% to 59.62%.
Things to check
- The interval assumes an appropriate model of independent observations. It does not establish representativeness.
- With zero successes, the upper bound does not automatically become zero: a finite sample cannot rule out rare successes.
Frequently asked questions
Is the margin always symmetric around the observed proportion?
No. The Wilson interval is built around an adjusted centre. The asymmetry is particularly visible for proportions close to 0 or 1.