Single proportion
Estimate a proportion and its confidence interval from a count and sample size. Compare methods to understand how CI width and coverage differ.
Wilson score — recommended in most situations. Maintains close-to-nominal coverage even for small n and extreme proportions. Slightly asymmetric around the estimate.
Wald — the textbook "p ± 1.96 SE" interval. Simple and symmetric, but can produce intervals outside [0,1] and under-covers for small n or p near 0 or 1. Avoid when n < 30 or p < 0.1 or p > 0.9.
Clopper-Pearson (exact) — guaranteed to contain the true proportion at the stated confidence level (conservative). Wider than Wilson in most cases. Preferred for regulatory submissions or when strict coverage guarantees are needed.