/** Two-Sample Approximate Score (Agresti-Coull) Confidence Interval **/

/********************************************
Macro to compute two-sample approximate score
(Agresti-Coull) confidence interval.
INPUT:
o y1,y2: number having characteristic in samples 1 and 2    
o n1,n2: sample size, samples 1 and 2
o conf_level: desired confidence level
OUTPUT:
o Point estimate of p1-p2
o Approximate score CI for p1-p2
*********************************************/
%macro ac2(y1,n1,y2,n2,conf_level);
data ac2;
tail_area=(1+&conf_level)/2;
z=probit(tail_area);
p1hat=&y1/&n1;
p2hat=&y2/&n2;
point_est=p1hat-p2hat;
n1_tilde=&n1+.5*z**2;
n2_tilde=&n2+.5*z**2;
p1_tilde=(&y1+.25*z**2)/n1_tilde;
p2_tilde=(&y2+.25*z**2)/n2_tilde;
se=sqrt(p1_tilde*(1-p1_tilde)/n1_tilde+p2_tilde*(1-p2_tilde)/n2_tilde);
ci_low=p1_tilde-p2_tilde-z*se;
ci_up=p1_tilde-p2_tilde+z*se;
run;
proc print noobs;
var point_est ci_low ci_up;
run;
%mend ac2;
/********************************************
Sample call using numbers from example in lecture notes:
%ac2(24,200,26,100,.95);
*********************************************/