Two Unexpected Multiple Hypothesis Testing Problems

https://astralcodexten.substack.com/p/two-unexpected-multiple-hypothesis

 

I.

Start with Lior Pachter's Mathematical analysis of "mathematical analysis of a vitamin D COVID-19 trial". The story so far: some people in Cordoba did a randomized controlled trial of Vitamin D for coronavirus. The people who got the Vitamin D seemed to do much better than those who didn’t. But there was some controversy over the randomization, which looked like this

Remember, we want to randomly create two groups of similar people, then give Vitamin D to one group and see what happens. If the groups are different to start with, then we won't be able to tell if the Vitamin D did anything or if it was just the pre-existing difference. In this case, they checked for fifteen important ways that the groups could be different, and found they were only significantly different on one - blood pressure.

Jungreis and Kellis, two scientists who support this study, say that shouldn't bother us too much. They point out that because of multiple testing (we checked fifteen hypotheses), we need a higher significance threshold before we care about significance in any of them, and once we apply this correction, the blood pressure result stops being significant. Pachter challenges their math - but even aside from that, come on! We found that there was actually a big difference between these groups! You can play around with statistics and show that ignoring this difference meets certain formal criteria for statistical good practice. But the difference is still there and it's real. For all we know it could be driving the Vitamin D results.