estimate: the estimated probability of success. null.value: the probability of success under the null, p. alternative: a character string describing the alternative hypothesis. The Clopper–Pearson interval is an early and very common method for calculating binomial confidence intervals. This calculator will compute the 99%, 95%, and 90% confidence intervals for a binomial probability, given the number of successes and the total number of trials. While being “exact” sounds better than “approximate”, the truth of the matter is that the Clopper-Pearson interval is generally wider than it needs to be, meaning you get a less precise interval: Exact Binomial and Poisson Confidence Intervals Revised 05/25/2009 -- Excel Add-in Now Available! (read below) Binomial || Poisson || Set Conf Levels. Please enter the necessary parameter values, and then click 'Calculate'. 7/21 a confidence interval for the probability of success. However, in cases where we know the population size, the intervals may not be the smallest possible. This is sometimes also called exact interval. Following Agresti and Coull, the Wilson interval is to be preferred and so is the default. This calculator relies on the Clopper-Pearson (exact) method. For instance, for a population of size 20 with true proportion of 50%, Clopper–Pearson gives [0.272, 0.728], which has width 0.456 (and where bounds are 0.0280 away from the "next achievable values" of 6/20 and 14/20); whereas Wilson's gives [0.299, 0.701], which has width 0.401 (and is 0.0007 away from the next achievable values). The PropCIs package has functions for calculating confidence intervals for a binomial proportion. 7/21  0.3333333. library(PropCIs) exactci(7, 21, conf.level=0.95) 95 percent confidence interval: 0.1458769 0.5696755. The "exact" method uses the F distribution to compute exact (based on the binomial cdf) intervals; the "wilson" interval is score-test-based; and the "asymptotic" is the text-book, asymptotic normal interval. Binomial Probability Confidence Interval Calculator. data.name: a character string giving the names of the data. The blakerci function uses the Blaker exact method. The Clopper-Pearson interval is based on quantiles of corresponding beta distributions. So I got curious what would happen if I generated random binomial data to find out what percent of the simulated data actually fell within the confidence interval. 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). The exactci function uses the Clopper–Pearson exact method. The reason for this is that there is a coverage problem with these intervals (see Coverage Probability). This page computes exact confidence intervals for samples from the Binomial and Poisson distributions. ... R.G. The arcsine interval is based on the variance stabilizing distribution for the binomial distribution. The logit interval is obtained by inverting the Wald type interval … A 95% confidence interval isn’t always (actually rarely) 95%. method = "exact" uses what’s called the Clopper-Pearson method, which uses the Binomial distribution to calculate an “exact” confidence interval rather than rely on an approximation. method: the character string "Exact binomial test".