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 |
I was surprised at 'sensitivity and specificity' (jointly) being considered different from 'false negatives and false positives' (jointly).
The given reasoning was about population differences, which.. fair enough, I understand that makes a difference, I just wasn't aware that was a standard difference in definition (if it is) and suggested the up thread commenter wasn't (or wasn't meaning to use it) either.
> 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
10%. 'inverse', as I called it, of 90%, not 95%.
(That's why I think you think I think (..!) that false negatives/positives rates are derivable from one another. Sorry if not and I'm just still not getting it...)
I don't think I am misunderstanding though - Wikipedia calls them 'true pos/neg rate', and gives formulae for false pos/neg rates as 1-true: https://en.m.wikipedia.org/wiki/Sensitivity_and_specificity
No, I think you're saying that the false negative rate as I defined it in my comment is the inverse of sensitivity. You've corrected me to say that you think the rate I defined is the inverse of specificity, which makes even less sense. And you did that despite the fact that I included a full calculation demonstrating that that isn't true.
Wikipedia's definition of the false negative rate differs from mine. Wikipedia indeed defines the false negative rate as (1 - sensitivity), though not, as you seem to believe, (1 - specificity). But you get no credit for this, because I explicitly defined what I meant by the false negative rate, and you echoed that definition in your response to my comment:
>>> your changed-order definitions
So: you think you haven't misunderstood what's happening. I ask you this: in my table above, I believe that prevalence is 20%, sensitivity is 95%, and specificity is 90%. Please verify that.
I have said that the conditional probability P(condition present | test negative) is 1.4%. You responded saying that that probability is actually 10%:
>> 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.
> 10%
Where are you getting that figure from? Show me in the table.
(Though it does seem a little odd to me to object to the comment on the basis of a definition you introduce yourself that even if some sort of standard is something that varies enough that Wikipedia uses a crucially different one.)