binom.coverage {binom} R Documentation

## Probability coverage for binomial confidence intervals

### Description

Determines the probability coverage for a binomial confidence interval.

### Usage

```binom.coverage(p, n, conf.level = 0.95, method = "all", ...)
```

### Arguments

 `p` The (true) probability of success in a binomial experiment. `n` Vector of number of independent trials in the binomial experiment. `conf.level` The level of confidence to be used in the confidence interval. `method` Either a character string to be passed to `binom.confint` or a function that computes the upper and lower confidence bound for a binomial proportion. If a function is supplied, the first three arguments must be the same as `binom.confint` and the return value of the function must be a `data.frame` with column headers `"method"`, `"lower"`, and `"upper"`. See `binom.confint` for available methods. Default is `"all"`. `...` Additional parameters to be passed to `binom.confint`. Only used when method is either `"bayes"` or `"profile"`

### Details

Derivations are based on the results given in the references. Methods whose coverage probabilities are consistently closer to 0.95 are more desireable. Thus, Wilson's, logit, and cloglog appear to be good for this sample size, while Jeffreys, asymptotic, and prop.test are poor. Jeffreys is a variation of Bayes using prior shape parameters of 0.5 and having equal probabilities in the tail. The Jeffreys' equal-tailed interval was created using binom.bayes using (0.5,0.5) as the prior shape parameters and `type = "central"`.

### Value

A `data.frame` containing the `"method"` used, `"n"`, `"p"`, and the coverage probability, `C(p,n)`.

### Author(s)

Sundar Dorai-Raj (sdorairaj@gmail.com)

### References

L.D. Brown, T.T. Cai and A. DasGupta (2001), Interval estimation for a binomial proportion (with discussion), Statistical Science, 16:101-133.

L.D. Brown, T.T. Cai and A. DasGupta (2002), Confidence Intervals for a Binomial Proportion and Asymptotic Expansions, Annals of Statistics, 30:160-201.

`binom.confint`, `binom.length`
```binom.coverage(p = 0.5, n = 50)