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yeah you need P(test|disease) to solve the problem.
The one that even fewer people appreciate is that you also need the false negative rate, which is not necessarily calculable from the false positive rate.
FNR = P(test=negative | disease=true) FPR = P(test=positive | disease=false)
They aren't the 1-minus of each other!
My friend wrote to me...
Turns out it’s not too hard to find the source. The bad news is twofold:
  1. The paper dates from 1978 so it’s almost a half a century old.
  2. It only involve a sample of 20 students.
The secondary source gets it wrong, reporting that there were only 10 students.
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haha, another good example of how urban legends spread.
I mean, I guess the overall message is true: people are bad at statistics. But the problem seems to run even deeper than what's implied... including how the original progenitors of this trial didn't give proper instructions, and how the results of the trial got propagated in incorrect ways, and then how it developed into this myth.
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