# A SAS Implementation of Confidence Intervals for Single Proportion: Eleven Methods

The following two papers by Professor Robert Newcombe, in my limit observation, are the most frequently cited papers in the industry for CI calculation:

This post serves as an implementation using SAS accompany with the first paper on confidence intervals for single proportion(method 1-7). Additional 4 methods also provided:

1.  Simple asymptotic, Without CC
2.  Simple asymptotic, With CC
3.  Score method, Without CC
4.  Score method, With CC
5.  Binomial-based, ‘Exact’
6.  Binomial-based, Mid-p
7.  Likelihood-based
8.  Jeffreys
9.  Agresti-Coull,z^22 successes
10. Agresti-Coull,2 successes and 2 fail
11. Logit

The codes are available at

It is a purely SAS/Base(data step and SQL) approach. I prefer data steps because it can be seamlessly incorporate into production work which looks like:

/r is the observed number of events/responders in n observations;/

%macro _Wald(r,n,alpha=0.05);

p=&r/&n;
z = probit (1-&alpha/2);
sd=sqrt(&np(1-p)); *Standard Deviation ;
se=sd/&n;            *standard error;
me=z*se;             *margin of error;
p_CI_low = p-me;
p_CI_up  = p+me;
p_CI=compress(catx(“”,”[“,put(round(p_CI_low,0.0001),6.4),“,”,put(round(p_CI_up,0.0001),6.4),“]”));
%mend _Wald;

data test;
input r n;
%_Wald(r,n);
keep r n p p_CI;
datalines;
81 263
15 148
0 20
1 29
29 29
;
run;

proc print data=test;run;

But when simulation required (in methods 6-7), some SQL clauses pop up. Admit that It makes the codes less elegant. In this situation, matrix operation language such as SAS/IML or R will do a better job.

Note that in SAS 9.2, PROC FREQ can produce the following five intervals(method 1, 3, 9 ,8, 5):

Wald (also with method 2)
Wilson
Agresti-Coull
Jeffreys
Clopper-Pearson (Exact)

For the five intervals in SAS 9.2, a good reference is Confidence Intervals for the Binomial Proportion with Zero Frequency by Xiaomin He and Shwu-Jen Wu:

Also, an equivalent R version of the eleven methods by Abteilung Kriminologie is also available at

Such R repository is also a good resource for SAS users. I almost “translate” R implementations directly to SAS for this post.