Small nitpick: > What we want to ask is: Given the ratings I have, there is a 95% chance that the “real” fraction of positive ratings is at least what? > Scor

Small nitpick: > What we want to ask is: Given the ratings I have, there is a 95% chance that the “real” fraction of positive ratings is at least what? > Score = Lower bound of Wilson score confidence interval for a Bernoulli parameter There is actually a 97.5% chance that the "real" fraction of positive ratings is at least X, because the Wilson interval is a confidence interval which excludes a tail at each extremum. I personally would prefer to use a Bayesian derivation and just compute a one-tailed statistic, rather than applying a CLT approximation out-of-the-box with no tailoring as is typical in frequentist statistics. Regardless though, the principles are much the same and the sorted result probably would match very closely, so if this computation is significantly faster than stick with that.