That error can creep in to diagnostics though. You can be at a 5 times increased risk for a very rare disease and it’s still overwhelmingly unlikely you have the disease.
Sometimes testing positive on a fairly accurate test for a very rare condition means you are still more likely to not have the condition, and even Doctors sometimes screw that logic up.
No, that's the first error. The usual base rate problem. I agree that it's a common mistake, but it's not the one I was trying to point out.
Knowing that this very rare disease affects 1 in 10_000 men, and 1 in 100_000 women, doesn't tell you that much about how to perform diagnosis on any one individual. But it does tell you accurately that the male ward probably needs 10x as many beds as the female ward.
No. Not what I was saying ... in my example the male ward needs no more beds than the female ward because the disease is ridiculously rare. I think we are inadvertently talking past each other.
Statistics are hard. At least for me.
Edit: also I wasn’t trying to respond directly/refute your comment. Just chiming in with a related concept.
OK maybe the beds is a bad example (maybe most of their occupants would be under observation... or there would be less than 1 per hospital). Let's say it's 90% fatal, and an outbreak occurs in a country where men are always buried in black coffins, and women in white.
Then we know what mix of coffins to load on the UN plane. But as a doctor on the ground, after your 99% accurate test comes back, you certainly need more information, and knowing the sex of the patient is not much help. The doctor, and the guy loading the plane, are asking very different questions.
Sometimes testing positive on a fairly accurate test for a very rare condition means you are still more likely to not have the condition, and even Doctors sometimes screw that logic up.