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I like Evan’s 2009 post a lot, but I like John’s analysis here even better. John seems to make fewer assumptions; in particular, Evan assumes a 95% confidence b

• wenc 3y ago
  In Evan’s derivation, which derives the lower Wilson confidence interval on a binomial distribution, the confidence level is a parameter — you can replace it with any level desired. He just happened to use 1.96 for 95%. John’s derivation is not based on the Wilson score but a Bayesian update on a beta distribution. They’re actually different algorithms. He starts a beta(1,1) and keeps updating. The advantage of John’s method is you get the variance as well but now to sort you have to technically calculate differences between normal distributions which is more involved (or you can ignore the variance and sort by the mean) Both work for normalizing sort order so that small samples don’t get biased. But as the sample sizes get larger they both converge to the expectation by the law of large numbers. I personally use the Wilson score method in my work and it’s easy to calculate and good enough for all practical purposes.