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Binomial confidence interval estimation - why is it not symmetric?

Are confidence intervals always symmetrical around the point estimate?

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This question is readily answered by a quick internet search on "confidence interval." For instance, Wikipedia links to en.wikipedia.org/wiki/Binomial_proportion_confidence_interval where non-symmetrical intervals are exhibited. A quick search on this site immediately answers the question. – whuber♦ Oct 5 '11 at 21:59

marked as duplicate by whuber♦ Oct 5 '11 at 22:02

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1 Answer

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Short Answer: No

Long Answer: It depends.

A confidence interval obtained from an analytical technique (a formula) will be symmetrical around the point estimate on a particular scale. For example, Hazard Ratios, Risk Ratios and Odds Ratios are symmetrical around the point estimate on the natural log scale. They aren't necessarily on other scales, which is often while you see them graphed on the log scale.

Confidence intervals obtained by other techniques, like bootstrapping, simulation, or credible intervals in Bayesian analysis, often are, but need not be.

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