It is worthwhile to note that with your 1/1000 prevalence and 5% false positive rate, if you test a population of 1000 you could(mathematically) get either 50 positives or 51. That is, there are 50 tests that will read positive whether the person has the condition or not and the person who has the condition might(1/20 chance) get one of those 50 tests.
Of course, pointing this out will make your rather elegant post a bit more complicated and less clear and certainly doing that math will lose some of your audience unnecessarily.
Thanks for reading. I was getting my *email limit* notice and had to trim a bit. OTOH, this stuff will get covered from some other perspectives and hopefully continue to clarify and elucidate.
My only caution is against writing probabilities "P(T)" or the like. It's not wrong, but it causes many to forget that there is no such thing as unconditional probability. I.e. all are like Pe(T|E) where the evidence E is made obvious.
(I'm way behind on everything. Haven't even got to your other yet.)
It is worthwhile to note that with your 1/1000 prevalence and 5% false positive rate, if you test a population of 1000 you could(mathematically) get either 50 positives or 51. That is, there are 50 tests that will read positive whether the person has the condition or not and the person who has the condition might(1/20 chance) get one of those 50 tests.
Of course, pointing this out will make your rather elegant post a bit more complicated and less clear and certainly doing that math will lose some of your audience unnecessarily.
Thanks for reading. I was getting my *email limit* notice and had to trim a bit. OTOH, this stuff will get covered from some other perspectives and hopefully continue to clarify and elucidate.
Love it, as always.
My only caution is against writing probabilities "P(T)" or the like. It's not wrong, but it causes many to forget that there is no such thing as unconditional probability. I.e. all are like Pe(T|E) where the evidence E is made obvious.
(I'm way behind on everything. Haven't even got to your other yet.)
I will ensure that I add in some appropriate emphasis on that as we move along, Professor! Cheers.