Build a Wilson score confidence interval for a survey proportion from the number of selected responses and total completed responses. Wilson intervals behave better than the basic Wald interval for modest samples and proportions near the boundaries. The calculator reports the observed proportion, both interval limits, and margin width without claiming that sampling error covers questionnaire bias or nonresponse bias.
Wilson center = [p̂+z²/(2n)]/[1+z²/n]. Half-width = z√[p̂(1−p̂)/n+z²/(4n²)]/[1+z²/n].
The primary result is conditional on the values and statistical assumptions entered. Read the secondary results to understand uncertainty, workload, or design sensitivity before making a decision.
This planning estimate is not a substitute for a study protocol, domain review, or a method chosen for the final data distribution.
For 240 selected responses out of 500, the estimate is 48.00%. At 95% confidence, the Wilson interval is approximately 43.65% to 52.38%.
The calculator uses a standard statistical approximation. Small samples, highly skewed outcomes, or model misspecification can make the estimate less accurate.
Yes. A 90% setting gives a narrower interval or lower sample requirement, while a 95% setting provides more conservative coverage.
Use zero only where the input allows it. A rate calculation still needs a positive total or a defined prior so that division by zero is avoided.
No. It summarizes uncertainty or planning assumptions; study design, randomization, measurement quality, and confounding still matter.
Keep rates and intervals at the shown precision, but round required counts upward because a fraction of a sample or processing unit is not usable.
| Item | How it is used |
|---|---|
| Observed or planned sample | Sets the available evidence or workload. |
| Uncertainty setting | Controls interval width or rejection threshold. |
| Variability or rate | Translates the sample into uncertainty, power, or capacity. |