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Peter_de_Blanc comments on Open Thread: February 2010 - Less Wrong
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If you're using Powerpoint, you might want to make a slide that says something like:
2,999 negatives -> 1% test positive -> 30 false positives
1 positive -> 99% test positive -> 1 true positive
So out of 31 positive tests, only 1 person has SDS.
If you've got the time, use a little horde of stick figures, entering into a testing machine and with test-positive results getting spit out.
Your numbers have me confused. I'd read the grandparent as implying 300M total population, out of which 3000 have the disease. (This is a hint to clarify the info in the grandparent comment btw - whether I've made a dire mistake or not.)
Another point to clarify is that the test's detection power isn't necessarily the inverse of its false positive rate. Here I assume "99%" characterizes both.
What I get: 300M times 1% false positive means 3M will test positive. Out of the 3000 who have the disease 30 will test negative, 2970 positive. Out of the total population the number who will test positive is 3M+2970 of whom 2970 in fact have the disease, yielding a conditional probability of .98 in 1000 that Steve has SDS.
I fail at reading. I thought it said "ONE in 3000 people in the US...."