While it makes some sense, it's not clear to me why those are different. If a test, say medical test, is correct 90% of time then chances of it being wrong is 10%.There are 4 events1. Test is +, patient has a disease2. Test is -, patient doesn't have a disease3. Test is +, patient doesn't have a disease4. Test is -, patient has a disease

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While it makes some sense, it&#039;s not clear to me why those are different. If a test, say medical test, is correct 90% of time then chances of it being wrong is 10%.There are 4 events1. Test is +, patient has a disease2. Test is -, patient doesn&#039;t have a disease3. Test is +, patient doesn&#039;t have a disease4. Test is -, patient has a disease

Calvin Maddox · Accepted Answer

To understand why the rate of false positives and false negatives should be different, you can consider the two edge cases: the constant tests.One “test” perform is by declaring every result a positive, regardless of any information about the input. Positive result no matter what. Clearly, in this case, we’re going to get a lot of false positives (unless the result really should be positive for everything in the population), but we’re not going to get any false negatives because we never report anything to be negative.Likewise, perform the “test” where every single result to be negative, and hence get a bunch of false negatives but it is impossible for me to get any false positives since never report anything as positive.In both of these tests it’s really obvious why the rate of false positives doesn’t match the rate of false negatives.In general any other test you perform can be thought of as some kind of piecewise combination of these two tests, so it’s actually really quite rare that you’d be able to construct a test with the same likelihood of false positives and false negatives.

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