Now, our true positive rate - taken from the police - is 80%. That means that out of our 15 "has drugs" people, we'll identify 15*0.8 = 12 correctly, and 15*0.2 = 3 incorrectly, like sopic.twitter.com/e2SFzTJ6aY
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This is why when you are testing for an uncommon outcome, your test has to be REALLY GOOD Drug sniffing dogs, even by the best estimates, are not
This goes doubly for screening large numbers of people. If you screen, say, everyone who goes into a music festival, you will likely catch few offenders but identify many totally innocent people
So what should we do to prevent harm from drugs if we know sniffer dogs are ineffective? Tons of things. I'll make another thread about these options if anyone's interested
Also P.S. I got a few pieces of terminology wrong - in particular, the first tweet should read "diagnostic test" not "intervention" - and also the "25% table" is slightly misleading as I've assumed that the negative predictive power is still 75% rather than 25%
P.P.S TL:DR version is that drug sniffer dogs, even when they get it right 80% of the time, still make more mistakes than "hits" when not that many people have drugs
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