## How to calculate 95% CI for a proportion of 100%

Occasional Contributor
Posts: 5

# How to calculate 95% CI for a proportion of 100%

Dear all,

Does anyone know how to calculate the 95% CI for a proportion when the proportion is exactly 100% ? Thanks !

Feng Liang

Super User
Posts: 10,784

## Re: How to calculate 95% CI for a proportion of 100%

``````data x;
x=1;output;
x=1;output;
run;
proc freq data=x;
table x/binomial cl;
run;``````
SAS Super FREQ
Posts: 4,243

## Re: How to calculate 95% CI for a proportion of 100%

The problem is that if all trials resulted in 'success' then (to a frequentist) the standard error is 0 and the confidence interval collapses to [1, 1]. There are ways to adjust the CI. See the Hanley's 1983 JAMA paper

http://www.medicine.mcgill.ca/epidemiology/hanley/reprints/If_Nothing_Goes_1983.pdf

which suggests that you should use a 95% CI of [1 - 3/n, 1] for the rate, where n is the number of observations.

SAS Employee
Posts: 386

## Re: How to calculate 95% CI for a proportion of 100%

You can get an exact lower confidence limit by using the EXACT BINOMIAL statement in PROC FREQ:

``````data a; input x w; datalines;
1 20
0 0
;
proc freq; table x; exact binomial; weight w; run;
``````
Occasional Contributor
Posts: 5

## Re: How to calculate 95% CI for a proportion of 100%

Thanks a lot for your help !

Regards,

Feng Liang

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