[OJFord]

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.

[thaumasiotes]

> 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

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%.

[OJFord]

I don't think I have, it sounds like you think I'm saying false negatives are the inverse of false positives? Not at all, that's obviously not true.

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

[thaumasiotes]

> it sounds like you think I'm saying false negatives are the inverse of false positives? Not at all, that's obviously not true.

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.

[OJFord]

Ok, fine, 'as you defined it'. It's hard to read your table on mobile. My only suggestion was that your definition might not be what the original commenter meant, because it's not my layman's understanding that they're different, but I don't know, maybe they also use your definition, no point arguing about it.

(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.)

[thaumasiotes]

> Though it does seem a little odd to me to object to the comment on the basis of a definition you introduce yourself

Notice that I always talk in terms of the question being asked. And your response to me was phrased in the same terms. You didn't say 10% was "the false negative rate", you said it was "the share of the time for which, when the test says 'no', the answer is 'yes'". You didn't say "the false negative rate is the inverse of the true positive rate"; you said "your changed-order definitions are just inverses [of each other]". Those claims are wildly false regardless of what you think "the false negative rate" means, for the simple reason that they make no reference to a "false negative rate".

> It's hard to read your table on mobile.

The table has four cells, eight if you count the labels. I have every confidence that you can do it.

[OJFord]

> > Though it does seem a little odd to me to object to the comment on the basis of a definition you introduce yourself

> Notice that I always talk in terms of the question being asked.

You were more specific, you replied to a commenter using 'false positive rate' as an undefined term; you introduced a definition. It's not the definition I'm familiar with; it's not the definition used on Wikipedia; I suggested it might (I don't know either!) be the definition intended by the commenter who used it.