Monday, March 08, 2021 9:13:32 AM
Here is why:
p-values mean nothing if you don't control for the number of statistical tests (the number of p-values you have computed) performed. Because, the more tests you perform, the higher the chance that you obtain, through pure random luck, a good p-value. Perform several dozen tests and I guarantee you that you will find good p-values in any random dataset. Hundreds and you have cured cancer, covid, and everything else. Of course, it's a fallacy, you have cured nothing. The p-value is just good because the company has performed heavy data mining without correcting the p-value accordingly.
To control for the number of tests, that we call the multiplicity, there are various correction methods, making different assumptions. Here the tests were designed post-hoc (=after a first look at the data), as opposed to the regular endpoint tests which were designed ex-ante (=before any look at the data). Consequently, the "standard" correction methods are Bonferroni and Holm-Bonferroni - smarter methods could have been used but only for tests designed ex-ante or under very strict conditions that are not met here.
With these method, to make it simple, for the best-ever p-value you get you have to multiply it by the number of tests performed - the multiplicity. In fact more than that because you already burned some alpha with the pre-designed tests performed (the regular endpoints which have all be missed), but I will be nice let's forget about that, it just makes things worse.
Reading the PRs and based on my experience, I think that the correction factor is certainly higher than 30, and probably in the 50-100 range.
So a p-value of 0.0319 is now, after the correction due to the datamining, above 0.6. Meaningless.
That's why I would advise any investor to take a course in statistics OR to avoid interpreting p-values at all. It's very easy to get tricked here. There are more subtleties than this, countless subtleties and traps.
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