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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?

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  • $\begingroup$ There's a fairly good introduction here $\endgroup$
    – Glen_b
    Commented Oct 15, 2013 at 22:17

2 Answers 2

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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)
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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")
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  • $\begingroup$ Of course, if you prefer a more commonly used (and more frequently updated) R package Hmisc, just run binconf(5, 12, method = "all") $\endgroup$
    – dwstu
    Commented Dec 27, 2013 at 15:45

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