binCI {binGroup} | R Documentation |

## Confidence Intervals for One Binomial Proportion

### Description

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

### Usage

```
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")
```

### Arguments

`n` |
number of trials (number of individuals under observation) |

`y` |
number of successes (number of individuals showing the trait of interest) |

`conf.level` |
nominal confidence level |

`alternative` |
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 |

`method` |
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. |

`tolerance` |
precision of computation for the bounds of the Blaker interval |

### Details

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.

### Value

A list containing:

`conf.int` |
the estimated confidence interval |

`estimate` |
the point estimator |

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

### Author(s)

Frank Schaarschmidt

### References

*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.

### Examples

```
# 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")
```

*binGroup*version 2.2-1 Index]