So I was catching up on emails today (and I apologize if you've emailed me in the past and didn't get a response but I struggle at emails). I got a great email from a college student on the Semenya case. He's an econ major and did some analysis on how absurdly high Semenya's tesosterone is as compared to the average female. It's mind boggling. According to his research, the IAAF's testosterone limit of 5nmol - and remember Semenya's actual # is way higher - is more than 50 standard deviations higher than what the normal woman possesses (Using two different sources, he came up with 58.79 and 144.3 standard deviations from the mean) assuming a normal distribution. He then tried to come up with a way to let non-stats people understand what that means. I loved his analogy:
College student wrote:
Yao Ming would be 22’6” tall to be 50 standard deviations from the mean height of males.
He showed his research to a friend who wondered if T might fall under a Poisson distribution so he re-did the work and found the IAAF limit to still be 34 and 25.77 standard deviations above the mean.
Despite my A+ in Econometrics at Princeton, my 80 on the PSAT math and my past experience as a high school math teacher, sadly I don't remember enough math to check his work, so can someone check out his math and see if it's correct? Also what type of distribution does T in woman follow? If it's Poisson, can someone come up with a height for say 25 standard deviations.
He explained his work in the following document. If it's confirmed, I'll post his name so we can give him credit.
https://docs.google.com/document/d/190WuasS8VNV65eY-OajegxJT6gI8qoFYqiX81eJaPAI/edit?usp=sharing