🧮 Clopper–Pearson Interval

Clopper–Pearson Interval#

An exact confidence interval for a binomial proportion.

Important

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What it is#

The Clopper–Pearson interval is the “exact” confidence interval for a binomial proportion — built directly from the binomial distribution (via Beta-distribution quantiles) rather than a normal approximation. It inverts the binomial CDF to find the proportions consistent with the data.

Its guarantee#

It never has less than the nominal coverage — a 95% Clopper–Pearson interval covers the true proportion at least 95% of the time for every p and n. That safety is its selling point when you must not under-cover.

The cost#

Guaranteeing coverage makes it conservative — the actual coverage is often ~99%, so the interval is wider than necessary and demands larger samples for a given precision. It is the widest of the common methods, best reserved for very small samples or when guaranteed coverage is essential.

Theme: Statistical Inference & Power · All terminology

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Mind map — connected ideas

Confidence Intervals (CIs) · Wilson Score Interval · Normal Distribution · Statistical Tests · Bootstrap Confidence Intervals (CIs) · Standard Error (SE)

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A Priori Power Analysis · Chi-square (χ²) Test · 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 · Significance Level (α)