binCI {binGroup}R Documentation

Confidence Intervals for One Binomial Proportion


Calculates the exact Clopper-Pearson and Blaker, the asymptotic second-order corrected, Wilson, Agresti-Coull and Wald confidence interval for a single binomial proportion


binCI(n, y, conf.level = 0.95, alternative = "two.sided",
 method = "CP")

binCP(n, y, conf.level=0.95, alternative="two.sided")
binBlaker(n,y,conf.level=0.95, tolerance=1e-04, alternative="two.sided")
binAC(n, y, conf.level=0.95, alternative="two.sided")
binSOC(n, y,conf.level=0.95,alternative="two.sided")
binWald(n, y, conf.level=0.95, alternative="two.sided")
binWilson(n, y,conf.level=0.95,alternative="two.sided")



number of trials (number of individuals under observation)


number of successes (number of individuals showing the trait of interest)


nominal confidence level


character string defining the alternative hypothesis, either 'two.sided', 'less' or 'greater' where 'less' gives the only an upper bound with confidence level=conf.level 'greater' gives the only a lower bound with confidence level=conf.level and 'two.sided' gives a two-sided confidence interval with confidence level=conf.level


character string defining the method for CI calculation: where "CP" is Clopper-Pearson, an exact tail interval showing symmetric coverage probability (inversion of two one-sided tests), "Blaker" is the Blaker interval, an exact interval, inversion of one two.sided test, therefore defined only two.sided, but shorter than the two-sided Clopper-Pearson CI. Both guarantee to contain the true parameter with at least conf.level*100 percent probability, "AC" is Agresti-Coull, generalized Agresti-Coull interval, asymptotic method, "Score" is Wilson Score, asymptotic method derived from inversion of the Score test, "SOC" is the second order corrected interval, asymptotic method for one-sided problems (for details see Cai, 2005), and "Wald" the Wald interval, which cannot be recommended.


precision of computation for the bounds of the Blaker interval


This function allows computation of confidence intervals for a binomial proportion from a standard binomial experiment. If an actual confidence level greater or equal to that specified in the conf.level argument shall always be guaranteed, the exact method of Clopper-Pearson (method="CP") can be recommended for one-sided and the improved method of Blaker (method="Blaker") can be recommended for two-sided hypotheses. If a mean confidence level close to that specified in the argument conf.level is required, but moderate violation of this level is acceptable, the Second-Order corrected (method="SOC"), Wilson Score (method="Wilson") or Agresti-Coull (method="AC") might be used, where SOC has the most symmetric coverage and Wilson and Agresti-Coull are in tendency conservative for the upper bound and proportions close to 0 and for the lower bound and proportions close to 1. The Wald CI might be used for large number of observations n>10000 or intermediate proportions.

For discussion of CI for a single binomial proportion see Brown et al. (2001) for two-sided and Cai (2005) for one-sided intervals.


A list containing:

the estimated confidence interval


the point estimator

And the method, conf.level and alternative specified in the function call.


Frank Schaarschmidt


Blaker H (2000) Confidence curves and improved exact confidence intervals for discrete distributions. The Canadian Journal of Statistics 28 (4), 783-798.

Brown LD, Cai TT, DasGupta A (2001) Interval estimation for a binomial proportion. Statistical Science 16 (2), 101-133.

Cai TT(2005) One-sided confidence intervals in discrete distributions. Journal of Statistical Planning and Inference 131, 63-88.

See Also

binom.test for the exact confidence interval and test, binTest to calculate p.values of the exact, Score and Wald test.


# Default method is the two-sided 95% Clopper-Pearson CI:

binCI(n=200, y=10)

# other methods might result in 
# shorter intervals (but asymetric coverage):

binCI(n=200,y=10, method="Blaker")
binCI(n=200,y=10, method="Score")

[Package binGroup version 2.2-1 Index]