Bill wrote:
ok, i think I am doing the math correctly below (although i've never taken a statistics class.
99.99% accuracy. 1 in 10,000 X 1 in 10,000 = 1 in 100,000,000. That's one false positive every 10,000 years (if there are 10,000 tests per year).
If it is 99.9% accurate, 1 in 1,000 X 1 in 1,000 = 1 in 1,000,000, which is one false positive every 100 years (assuming 10k tests per year again).
I teach stats, but this is something anyone who took HS biology should be able to do -- think Punnet squares.
Yep, there would be that many false positives. BUT another issue is false negatives, which is what I think happened with Bernard Lagat.
They put together the tests in such a way as to make it much easier to get a false negative than false positive -- it's just the general nature of the modern legal system to nail you only if we're really sure. So let's say there's 1% false negatives. 1% of cheaters' A samples come out negative and they get out of jail free. Of the cheaters who got caught, 1% of their B samples come out negative and they get off. That's 1.01% free who should be nailed.
But I'll say that the rates of false positives and false negatives are much higher than that. 99.99% is an unbelievably high threshhold of success, and even 99.9% is pretty tough. I'm willing to bet that as much as 10% of the tests on dopers come back negative (or inconclusive), which mean 11% come out of the testing unpunished.