binom.midp {binomSamSize} R Documentation

## Calculate mid-p confidence interval for binomial proportion

### Description

Calculate mid-p confidence interval for the the binomial proportion based on one observation from the binomial distribution

### Usage

binom.midp(x, n, conf.level=0.95)


### Arguments

 x Vector of number of successes in the 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

### Details

The function uses uniroot to determine the upper and lower bounds of the mid-p confidence interval.

The lower bound p_l is found as the solution to the equation

\frac{1}{2} f(x;n,p_l) + (1-F(x;m,p_l)) = \frac{α}{2}

where f(x;n,p) denotes the probability mass function (pmf) and F(x;n,p) the (cumulative) distribution function of the binomial distribution with size n and proportion p evaluated at x. In case x=0 then the lower bound is zero.

The upper bound p_u is found as the solution to the equation

\frac{1}{2} f(x;n,p_u) + F(x-1;m,p_u) = \frac{α}{2}

In case x=n then the upper bound is 1.

### Value

A data.frame containing the observed proportions and the lower and upper bounds of the confidence interval. The style is similar to the binom.confint function of the binom package

M. Höhle

### References

S. E. Vollset (1993), Confidence intervals for a binomial proportion, Statistics in Medicine, 12, 809–824

Fosage, G.T. (2005) Modified exact sample size for a binomial proportion with special emphasis on diagnostic test parameter estimation, Statistics in Medicine 24(18):2857-66.

A. Agresti and A. Gottard (2005), Comment: Randomized Confidence Intervals and the Mid-P Approach, Statistical Science, 20(4):367–371

### Examples

binom.midp(x=0:10,n=10)
binom.midp(x=0:5,n=5,conf.level=0.9)


[Package binomSamSize version 0.1-5 Index]