# How can I calculate the standard error of a proportion?

I made a comparison of hatch success between 2 populations of birds using R's prop.test() function:

prop.test(c(#hatched_site1, #hatched_site2),c(#laid_site1, #laid_site2))


It gave me the proportions of each site as part of the summary. How can I calculate the standard error for each proportion?

• Do you mean the standard error for each proportion? If this is what you are looking for, then this webpage might be of interest for you: Interval Estimate of Population Proportion May 20, 2011 at 1:11
• That'll do! I can calculate SD from SEM. I suppose I could've done the same to calculate SEM from the 95% confidence interval provided by prop.test too, but this is better. Thanks @Bernd!
– Mog
May 20, 2011 at 2:22
• Nooo! As @Bernd noted, the proportion does not have a standard deviation. Or more precisely, it does, but it is called the standard error. Standard deviation refers to the variability of the original 0-1 variable. May 20, 2011 at 2:55
• Oh! Wow, thanks for the clarification @Aniko...that wouldn't have been good to report. Ok, I'll stick with the standard error. Thanks again!
– Mog
May 20, 2011 at 3:43
• Even more precisely, "standard error" of the proportion refers to the standard deviation of the distribution of the sample proportions from random samples of the particular sample size from the population of interest. May 20, 2011 at 15:55