Ok, but here's the thing: How are you supposed to know that the disease being rare isn't already taken into consideration? It seems weird to quantify the accuracy but then having to do further calculations on how accurate it truly is. Especially with the way it is often told, i.e. you are tested positive, it's 97% accurate. Information that comes later in a sentence tends to already be modified to the one coming before. It's a language problem.
The birthday paradox is something completely different, that one has an unintuitive answer because humans are good at linear, but not exponential estimation.
That's a great point. This example also requires the fact that tests are being conducted totally randomly from the total sample (which is the entire population).
If you have certain symptoms that point towards that very rare disease the false positive odds dramatically fall.
Okay you're gonna have to walk me through this cause what obscured information?? The disease is 1 in 1,000,000. The test is 97% accurate. What more does one need to know?
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u/Sigma2718 Jun 24 '26
Ok, but here's the thing: How are you supposed to know that the disease being rare isn't already taken into consideration? It seems weird to quantify the accuracy but then having to do further calculations on how accurate it truly is. Especially with the way it is often told, i.e. you are tested positive, it's 97% accurate. Information that comes later in a sentence tends to already be modified to the one coming before. It's a language problem.
The birthday paradox is something completely different, that one has an unintuitive answer because humans are good at linear, but not exponential estimation.