Estimate the statistical power of a one-sample survey proportion test for a planned sample size and meaningful difference from a benchmark. The approximation compares the alternative proportion with the null benchmark using a two-sided normal test. It is useful for early planning and sensitivity checks, though exact tests or simulation may be preferable for small samples or proportions near zero or one.
SE under the alternative = √[p₁(1−p₁)/n]. The rejection boundary uses zα/2√[p₀(1−p₀)/n]. Power is approximated from the normal probability of falling beyond either two-sided boundary.
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.
With 500 responses, a 50% benchmark, a 56% alternative, and 5% significance, the approximation gives roughly 77% power.
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. |