3 ms·
The problem is that "99% the time gives a correct result" is imprecise. It can be understood as both: - p(sick|positive) = 0.99 - p(positive|sick) = 0.99 We
by cdancette 8y ago
The problem is that "99% the time gives a correct result" is imprecise.
It can be understood as both:
- p(sick|positive) = 0.99
- p(positive|sick) = 0.99
We get totally different results, the first one is obvious (99% change of being sick), and the second one needs Bayes' Theorem (and is the one we want to use).
- thaumasiotes 8y agoI would only interpret "the test gives a correct result 99% of the time" to mean that out of every 100 test results, 99 are correct and one is wrong. Neither of your interpretations matches that. You need all kinds of additional information to say anything more specific. "99% of results are correct" can easily be true while p(sick | positive) and p(positive | sick) each vary anywhere between 0 and 1.