binom.midp {binomSamSize} | R Documentation |
Calculate mid-p confidence interval for the the binomial proportion based on one observation from the binomial distribution
binom.midp(x, n, conf.level=0.95)
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 |
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.
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
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
binom.midp(x=0:10,n=10) binom.midp(x=0:5,n=5,conf.level=0.9)