Syntax and formula for the 99% confidence interval for a proportion

#1
According to: https://www.mccallum-layton.co.uk/t...nfidence-interval-for-proportions-calculator/

The 99% confidence interval for 23 out of 125 is: +-8.93, where observed proportion is 23/125=18.4%.

When I try and replicate this in Stata, with reference to this: http://www.stata.com/manuals13/rci.pdf

I enter: cii 125 23 ,level(99)

Which gives me binomial exact 0.1042... and 0.2887

I don't get it. Is my syntax wrong? What does binomial exact mean? Is that the reference range I'm being shown?

Has anyone got an equation for the confidence interval handy? All I can find in my lecture notes and online is a formula for if you have the mean and standard error etc etc
 

bukharin

RoboStataRaptor
#2
There are different methods for calculating the confidence interval for a proportion, and they give you slightly different results. Have a look at the PDF manual for -cii-. By default it's using the binomial distribution to calculate an "exact" confidence interval. If you add the "wald" option you'll get the same result as the web calculator.