What CI methods exist for a proportion?

medium

Answer

$Wald (naive): p̂ \pm z * \sqrt(p̂(1-p̂)/n) — bad when p̂ is near 0/1 or n small (can even exceed [0,1]).$
$Wilson score: preferred default; more accurate coverage.$
$Clopper-Pearson (exact): guaranteed conservative coverage but wider.$
$Agresti-Coull: quick fix (add 2 successes + 2 failures).$
$Modern practice: use Wilson or Clopper-Pearson, avoid Wald except for very large n and mid-range p.$

Check yourself — multiple choice

Only Wald
Wald (naive, bad near 0/1) / Wilson (default) / Clopper-Pearson (exact, conservative) / Agresti-Coull; avoid Wald with small n or extreme p̂
Same as z-test
Not needed

Proportion CIs: Wilson or Clopper-Pearson preferred; avoid Wald at extremes.

#confidence-interval

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