Mathemagic

Math may not always be as simple as we might think.

Example from shiftless2 mathematician PhD 14/07/31

Q: Consider a rare disease, one that affects 1% of the population
There is a test for the disease that is 99% accurate. That is, 99% of the time it gives the “right” answer and the remaining 1% of the time it gives the wrong answer.
Someone is tested for the disease and tests positive (i.e., the test says they’re ill) so the doctor sends them for a retest. Should that individual be panicking, cautiously optimistic, or what?

I have no idea who/what “shiftless2 mathematician PhD 14/07/31” is. Is it a quote from another site, or from a magazine or what?

He should be going to get the retest done. What do his emotions have to do with the math? He should be like anyone else, concerned that the first test did not establish that he was uninfected.

That’s a weird test, and it’s a weird place for this question.

Take a population of 10,000 people. 100 people will have the disease.

Of the remaining 9,900, if they all take the test, 99 will test positive incorrectly.

Of the 100 who have the disease, 99 will test positive correctly.

If you test positive, all other factors being equal, the chances are even that you are in either group, yes?

So you should be freaking the hell out (if the disease is serious): your chances of having a nasty disease just went from 1% to 50%!

But that presupposes that the test is given to everyone, and that it’s the only basis for diagnosis. Few tests are like that. If you’re given a medical test, chances are very high that you’re showing some symptoms of the condition already, or you’ve got family member with the disease, or something like that.

Also, what sort of weirdo test has equal chances for false positives and false negatives?

I can’t determine if this is an actual topic for debate. As it stands, because of the lack of readability, I’m not sure it’s suitable anywhere. I’m going to close it for now and invite sear to PM me if they’d like to reframe the debate or OP in a way that is more suitable for another forum.

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