coverage {binomSamSize} R Documentation

## Calculate coverage probability for a binomial proportion confidence interval scheme

### Description

For a given true value of the proportion compute the coverage probability of the confidence interval

### Usage

```coverage(ci.fun, n, alpha=0.05, p.grid=NULL,interval=c(0,1),
pmfX=function(k,n,p) dbinom(k,size=n,prob=p), ...)
## S3 method for class 'coverage'
plot(x, y=NULL, ...)
```

### Arguments

 `ci.fun` `binom.confint` like function which computes confidence intervals for a binomial proportion. `n` Sample size of the binomial distribution. `alpha` Level of significance, 1-α is the confidence level. `p.grid` Vector of proportions where to evaluate the confidence interval function. If `NULL` all those values where the minimum coverage probability can occur is taken. If not `NULL` then the union between `p.grid` and these values is taken. `interval` Vector of length two specifying lower and upper border of an interval of interest for the proportion. The intersection of the above grid and this interval is taken. `pmfX` A function based on the arguments `k`, `n` and `p`, giving the probability mass function (pmf) f(x;n,p)=P(X=k;n,p) of X. Typically, this will be the pmf of the binomial distribution. `x` An object of class `coverage` `y` Not used `...` Further arguments to be sent to `ci.fun` or the plot function

### Details

Compute coverage probabilities for each proportion in `p.grid`. See actual function code for the exact details, which `p.grid` is actually chosen.

### Value

An object of class `coverage` containing coverage probabilities, coverage coefficient and more.

M. HÃ¶hle

### References

Agresti, A. and Coull, B.A. (1998), Approximate is Better than "Exact" for Interval Estimation of Binomial Proportions, The American Statistician, 52(2):119-126.

### Examples

```#Show coverage of Liu & Bailey interval
cov <- coverage( binom.liubailey, n=100, alpha=0.05,
p.grid=seq(0,1,length=1000), interval=c(0,1), lambda=0, d=0.1)
plot(cov, type="l")

#Now for some more advanced stuff. Investigate coverage of pooled
#sample size estimators
kk <- 10
nn <- 20
ci.funs <- list(poolbinom.wald, poolbinom.logit, poolbinom.lrt)
covs <- lapply( ci.funs, function(f) {
coverage( f, n=nn, k=kk, alpha=0.05, p.grid=seq(0,1,length=100),
pmfX=function(k,n,p) dbinom(k,size=n, p=1-(1-p)^kk))
})

par(mfrow=c(3,1))
plot(covs[[1]],type="l",main="Wald",ylim=c(0.8,1))
lines(c(0,1),rep(0.95,2),lty=2,col=2)
plot(covs[[2]],type="l",main="Logit")#,ylim=c(0.8,1))
lines(c(0,1),rep(0.95,2),lty=2,col=2)
plot(covs[[3]],type="l",main="LRT",ylim=c(0.8,1))
lines(c(0,1),rep(0.95,2),lty=2,col=2)

poolbinom.wald(x=1,n=nn,k=kk)
poolbinom.logit(x=1,n=nn,k=kk)
poolbinom.lrt(x=1,n=nn,k=kk)

```

[Package binomSamSize version 0.1-5 Index]