4 ms·
The confidence region appears symmetric around the mean. This indicates they are using the normal approximation. Exact confidence regions can be found, if you
by altrego99 13y ago
The confidence region appears symmetric around the mean. This indicates they are using the normal approximation.
Exact confidence regions can be found, if you do it using Binomial instead.
The question to be asked, if m out of n is the frequency, is for which values of p do you have P(m>=M) = 0.975 and for which value of p do you have P(m<=M) = 0.975, where M ~ Binimial(n,p).
It can be solved easily too.
- jessicaraygun 13y agoHey, I'm the author of Confidence.js which was used to power this A/B testing calculator. That sounds really interesting and worth looking into - thanks for the feedback!
- cheesycheese 13y agoThe normal approximation is notoriously [1][2] bad when the binomial proportion you're trying to estimate is small and you don't have a big n. If one still wants a closed-form out-of-the-box formula (to avoid the exact resolution you suggested), one can use the Wilson approximation for instance. [1]: http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval http://en.wikipedia.org/wiki/Binomial_proportion_confidence_... [2]: http://projecteuclid.org/download/pdf_1/euclid.ss/1009213286 http://projecteuclid.org/download/pdf_1/euclid.ss/1009213286