# Wilson CI for a proportion p, based on observing n.positive positives in srs of n

# see Rothman 2002 p 132

wilson.ci = function(n.positive, n, conf.level=0.95){
z=qnorm(conf.level+(1-conf.level)/2);
p.hat=n.positive/n; q.hat=1-p.hat;
plus.minus = c(-1,1) * z * ( p.hat*q.hat/n + (1/4)*(z/n)^2 )^0.5;
ci = ( n/(n+z^2)) * ( p.hat + (z^2)/(2*n) + plus.minus );
return(ci) 
}

# Rothman examples (p 132 and q 2 p 142)

wilson.ci(1,20,0.90)

wilson.ci(0,30,0.90)