re: #180 Belafon

I’m really leaning toward the idea that everyone needs to take a semester on Bayes Theorem. I can’t really think of a better way to show how bad humans are at reasoning than to show how easy it would be for a 96% accurate drug test to put you in jail.

This really shouldn’t take a semester to do. For example, lets suppose we have a 99% accurate drug test that is administered to 1,000,000 people, and that 10% of these 1,000,000 people are drug users.

Simplifying things a bit, the results will be:

99,000 people correctly identified as drug users.

1,000 people incorrectly identified as non-drug users.

891,000 people correctly identified as non-drug users.

9,000 people incorrectly identified as drug users.

So if all that is known about someone from this group of people is that they failed the drug test, the chance that they are actually a drug user is 99/108, which is about a 9% false positive rate. This false positive rate is much greater than the 1% error rate one would naively expect from the raw accuracy of the test.