p-values (part 3): meta distribution of p-values
So far we have discussed what p-values are and how they are calculated, as well as how bad experiments can lead to artificially small p-values. The next thing that we will look at comes from a paper by N.N. Taleb (1), in which he derives the meta-distribution of p-values i.e. what ranges of p-values we might expect if we repeatedly did an experiment where we sampled from the same underlying distribution.
The derivations are pretty in depth and this content and the implications of the results are pretty new to me, so any discrepancies/misinterpretations found should be pointed out and/or discussed.
Thankfully, in this video (2) there is an explanation that covers some of what the paper says as well as some Monte-Carlo simulations. My discussion will focus on some simulations of my own that are based on those that are done in the video.
What we are talking about
We have already discussed what p-values mean and how they can go wrong.…