citation to Agresti and Min
Agresti, A. and Min, Y. (2005). Simple improved confidence intervals for comparing matched proportions. Statistics in Medicine 24, 729-740.
--- a portion of a Google cached U.Fla web site, probably by Agresti
R code for the adjustment of the Wald confidence interval for a difference of proportions, with matched pairs. This is the interval called Wald+2 in Agresti and Min, Statistics in Medicine, 2004, which adds 0.5 to each cell before constructing the Wald CI. The CI is truncated when it overshoots the boundary.
diffpropci <- function(b,c,n,conflev)
{
z <- qnorm(1-(1-conflev)/2)
diff <- (c-b)/(n+2)
sd <- sqrt((b+c+1)-(c-b)^2/(n+2))/(n+2)
ll <- diff - z*sd
ul <- diff + z*sd
if(ll < -1) ll = -1
if(ul > 1) ul = 1
c(ll, ul)
}
# Adjusted Wald interval for difference of proportions with matched pairs
# "conflev"=confidence coefficient, n=sample size, b,c = off-diag countsend extract from Agresti's site