Determines the probability coverage for a binomial confidence interval.

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

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"`

A `data.frame`

containing the `"method"`

used, `"n"`

, `"p"`

,
and the coverage probability, `C(p,n)`

.

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"`

.

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.

```
# NOT RUN {
binom.coverage(p = 0.5, n = 50)
# }
```

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