Wilson Score Interval#
An accurate confidence interval for a proportion, robust for small samples.
Important
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What it is#
The Wilson score interval is a well-calibrated confidence interval for a binomial proportion, derived by improving the crude normal-approximation (Wald) interval. Introduced by E. B. Wilson in 1927, it is asymmetric and always stays within [0, 1].
Why it’s better#
Unlike the Wald interval, it doesn’t overshoot past 0 or 1 and doesn’t collapse to zero width when the observed proportion is 0 or 1; and unlike Clopper–Pearson, it isn’t overly conservative — its coverage sits close to nominal, so its intervals are narrower. That balance makes it the recommended default in most applications.
The caveats#
Its coverage can dip slightly below nominal for a few awkward proportions, and for extremely small samples the guaranteed Clopper–Pearson may still be safer. A continuity-corrected variant exists for tighter coverage.
Theme: Statistical Inference & Power · All terminology
Hint
Mind map — connected ideas
Confidence Intervals (CIs) · Clopper–Pearson Interval · Normal Distribution · Standard Error (SE) · Z-Score · Statistical Tests
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More in Statistical Inference & Power
A Priori Power Analysis · Chi-square (χ²) Test · Clopper–Pearson Interval · Compromise Power Analysis · Confidence Intervals (CIs) · Effect Size (δ) · Hypothesis Testing · Kolmogorov–Smirnov (KS) Test · Minimum Detectable Lift (MDL) · P-Value (probability value) · Post Hoc Power Analysis · Power (1 – β) · Power Analysis · Sample size
See also
Source article Adapted (context, re-expressed) in our own words from: Wilson Score Interval (insightful-data-lab.com).