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Is it true that Wilson score interval with continuity correction is strictly conservative? I mean, is its actual coverage probability always not less than its nominal confidence coefficient?

UPDATE: no, see Newcombe (1998) http://www.stats.org.uk/statistical-inference/Newcombe1998.pdf

If not, are there confidence intervals for binomial proportion which are 1) strictly conservative, 2) easily computable by explicit formulas, 3) of practical value?

For the Agresti-Coull interval, it is known that its actual (minimum) coverage probability depends on n and is less than its nominal confidence coefficient. Is it known whether the actual coverage probability approaches the nominal confidence coefficient as n goes to infinity?

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    $\begingroup$ In case you don't get an answer here, try stats.stackexchange.com $\endgroup$
    – Someone
    Commented May 26, 2011 at 7:31
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    $\begingroup$ Or, speaking more blatantly, I doubt many people here understand even half of the words you used (I certainly don't). I suspect that you ask something not too hard to figure out, but the language you speak is the internal language of statistics, which severely restricts the group of people who might be able to answer. Actually, I can think of just 3 on this site. They may eventually answer but the chance is not terribly high. Remember that you ask a mixed audience, not just one specialist in your particular field when posting on MO and other math. sites :) $\endgroup$
    – fedja
    Commented May 26, 2011 at 13:40

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You can obtain a strictly conservative coverage interval if you use inverse binomial sampling, i.e. allow sample size not to be fixed. See this answer, or this paper.

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