![]() Stata by default ranks lowest value as 1 and given ties splits ranks to preserve the sum of the ranks. In $n$ trials when the probability of a success on one trial is $p$. Note that binomialtail($n,k,p$ ) is here the probability of observing $k$ or more successes Code in any other software should be simple. Here is a worked example with Stata code. Substantively, it remains possible that the number of completions provides a better measure. It can be interpreted as a standard problem. 1 head out of 1 is less convincing than 17 out of 20. It's a little like evaluating magicians judged on their ability to produce heads every time on tossing a coin. Therefore you can, given some overall probability of success (which can only be estimated from the data, so far as I can see on your information), estimate tail probabilities for each person on a binomial model. that 1/1 is more consistent with chance (or luck or good fortune) than 17/20. ![]() The argument is, in your example of users 1 and 2, that 1/1 deserves less credit than 17/20, i.e. The central question is ranking how well people did.
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