function [upperlim,lowerlim]=agresti_coull_binomial_confidence_interval(num_successes,num_attempts)
%based on adding 2 successes and 2 failures before computing the Wald CI;  American Statistician 1998
%checked aug 2/2007

z=1.96;
%z=abs(qnorm(1-confidence_level/2)) -- this is s code, using confidence level as input
ptilde=(num_successes+2)/(num_attempts+4);
stderr=sqrt( (ptilde*(1-ptilde)) /(num_attempts+4));
upperlim=ptilde+(z*stderr);if(upperlim > 1), upperlim=1;end
lowerlim=ptilde-(z*stderr);if(lowerlim < 0), lowerlim=0;end