[c_moscardi]

Yep, my read too. The code he provides is definitely the Clopper-Pearson formula. [1]

This confused me as well, since I've always used the normal central-limit-based confidence interval for binary outcomes.

[1] https://en.wikipedia.org/wiki/Binomial_proportion_confidence...

(I am no expert in the analytic underpinnings of the beta distribution or precisely how it is the conjugate prior to the binomial -- or, rigorously speaking, what conjugate prior means -- but the formula here lines up with his formula :P )