binomSamSize (version 0.1-3)

coverage: 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), ...)
"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, $1-\alpha$ 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

Value

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

Details

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

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)