# Fraction confidence intervals for small sample size

What is 95% confidence interval for the fraction of 5 successes out of 12 trials?

Is it possible to compute confidence intervals for a sample of this size?

It is certainly possible to do this. There are several methods. The literature is surprisingly large; for a good entry point see Agresti & Coull (1998)

If you are using R you can use this:

install.packages("binom")
library(binom)
binom.confint(5, 12)


Without the binom package, just run the following to get the 95% confidence interval using the "exact" method (Clopper-Pearson method)

binom.test(x = 5, n = 12)\$conf.int
# same as binom::binom.confint(x = 5, n = 12, methods = "exact")

• Of course, if you prefer a more commonly used (and more frequently updated) R package Hmisc, just run binconf(5, 12, method = "all") – dwstu Dec 27 '13 at 15:45