Earlier quoted context omitted.
> Its lunacy for tests to be regulated beyond requiring rough false positive false negative rates There is a good reason tests are described in terms of sensitivity and specificity ("if the answer in reality is yes, how often will the test say no?") rather than in terms of false positive or false negative rates ("if the test says no, how often is the true answer yes?"). The sensitivity and specificity are facts about…
I'm not sure GP was intending to make that distinction (rates globally for the test vs. the sample population being tested by.. what a given doctor/hospital?) - I haven't come across that before. If the population is the same then your changed-order definitions are just inverses, and they're just different terms for the same thing.
> If the population is the same then your changed-order definitions are just inverses
No, you just haven't understood the concept.
Let's assume some condition has a prevalence of 20%, and a test for it will correctly identify presence of the condition 95% of the time, while correctly identifying absence of the condition 90% of the time. We can immediately answer the first question: when the answer is "yes", the test will say "no" 5% of the time.
You have proposed that when the test says "no", the answer is "yes" a share of the time that might be the inverse of 5%, or perhaps 5% itself. I have no idea what you meant -- and I suspect you didn't either -- but the correct rate of false negatives is not 5%, 95%, nor 2,000%.
In a model population of 10,000 people, we will see this:
| condition present | absent |
test positive | 1900 | 800 |
negative | 100 | 7200 |
From this table we can see that the false negative rate is 100/7300 or 1.4%. The false negative rate looks much better than the sensitivity and specificity figures because the condition is rare. The corollary to that is a horrific false positive rate of 800/2700 = 30%.