PHARM/PCS V5 · Procedure 43 Pairwise and Nonparametric
Proportions: Confidence Limits
Put exact confidence limits on a single proportion, such as a response rate, that stay within 0 and 1 even for small samples.
What it computes
Computes confidence limits for a proportion p = m/N using the exact formula (Equations 43.2-43.5) with continuity correction.
Inputs and outputs
You provide
- Number responding m
- Total subjects N
- A confidence level
PHARM/PCS reports
- The proportion p = m/N
- Its exact, asymmetric confidence limits
When to use it
When you have a single proportion (response rate, incidence, hit rate) and need a confidence interval around it. It pairs naturally with the chi-square test (Procedure 42) when you move from estimating one proportion to comparing categories.
Reading the results
These exact limits are asymmetric, especially for small N or proportions near 0 or 1, where a symmetric interval would spill past the 0-to-1 bounds; the asymmetry is a feature. The narrower the interval you need, the larger the N required, and near the extremes that requirement grows steeply.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.