2019年9月25日 · The Clopper–Pearson interval is an early and very common method for calculating binomial confidence intervals.[8] This is often called an 'exact' method, because it is based on the cumulative probabilities of the binomial distribution (i.e., exactly the correct distribution rather than an approximation).

2022年10月25日 · Confidence intervals are identical because number of trials, number of successes, and $\alpha$ are the same. In the linked text, it shows "a more common way to represent the Binomial Exact CI," using the relationship between the binomial CDF and the beta distribution (aka Clopper-Pearson Method). A similar formula:

2014年2月25日 · I was wondering if anyone can explain to me the intuition beyond the Clopper-Pearson CI for proportions. As far as I know, every CI includes a variance in it. However, for proportions, even if my proportion is 0 or 1 (0% or 100%), the Clopper-Pearson CI …

2015年9月10日 · The using of beta distribution to construct the limits of the Biomial Proportions (Clopper-Pearson Formula) is ilustrated in the article "Confidence Bounds & Intervals for Parameters Relating to the Binomial, Negative Binomial, Poisson and Hypergeometric Distributions" by Fritz Scholz (2008). You can get it from:

2022年1月19日 · The resulting confidence interval for the sensitivity was 95.55% - 100.00% even though the sensitivity for the sample is 100%. This seems off and I'm wondering if this is due to methodology (from the website's documentation it creates exact Clopper Pearson intervals) not being well defined for extreme values like this one.

Clopper-Pearson is an exact binomial method and can be used to get confidence intervals for p even when the number of successes is 0 out of N or N out of N. in the first case it will give an interval from 0 to A where A depends on N and alpha and from B to 1 in the latter case.

2020年7月6日 · Accuracy is not a single binomial proportion, so the Clopper-Pearson interval does not apply. In contrast to Normal and Poisson, the sum of two binomial random variables with different means is not (in general) a binomial. You can use a confidence interval based on the Normal approximation, preferably after some transformation like logit.

2015年5月21日 · The paper presented results using the exact (Clopper-Pearson) interval. I verified that the exact interval would give the results described (202 out of 202 yields an upper 95% confidence bound of 0.9853, which they reported to be 98.5%, and 198 out of 199 gives 0.9764, which they reported as 97.6%). So far, so good.

@Joris also mentioned the "exact" Clopper-Pearson intervals and gave you a reference which looks very nice. There is another confidence interval for proportions which you will likely encounter (note it is also not symmetric), the "Wilson" interval which is a type of asymptotic interval based on inverting the score test.

2022年2月15日 · $\begingroup$ I am voting to reopen the question as the answers linked by @whuber do not explain the Clopper-Pearson confidence intervals provided by the function binom.test() in the stats package, which - in contrast to the approaches mentioned there - belongs to the standard installation of R. $\endgroup$ –