That's a whole thing in statistics:

https://en.wikipedia.org/wiki/Power_of_a_test

First, I did not find any statistical test in the paper. The sample size is not relevant.

Further the power of a test already required you to know two parameters: variance and the size of the effect your testing for (difference between means). Proctorio is very careful in not claiming any effectiveness for detecting cheaters, how will you estimate these parameters?

Also iirc, the rule of thumb was for a normal distribution 30 samples is enough for decent strength, 40 samples is enough for general distributions unless you're looking at very small effects, weird distributions or in very noisy experiments.

Right, I'm trying to do this sorcratically and we got a smarty-pants over here. HN constantly has sample size critiques without power analysis responses which is a shame.

I'm quick to this sort of judgment myself, so I feel confident advising you that I don't necessarily think the person was trying to be snarky.

Oh no, not at all. It was hilarious to have someone jump in earnestly. If anything i was the one being duplicitous with a leading question.

There are very well documented formulas for calculation sensitivity and specificity of a diagnostic with a certain degree of certainty around it. You would use one of those.