The concepts of positive and negative selection are not quite well defined in your essay, I think.
Imagine that you have one test, with a gaussian distribution of outcomes. Let’s arbitrarily set a threshold, and if people are above this threshold, they have passed this test. Call the sets of passing A and not passing ~A
Would you call this a positive or negative selection? It is neither, in my opinion.
Now, imagine you have two tests, A and B.
A positive test is one where A U B are selected.
A negative test is one where ~(~A ^ ~B) are selected.
In other words—the operative difference between positive and negative selection is OR vs. AND.
Nice step toward clarity, but the leading example contrasts a single-test positive selection rule versus a multiple-test negative selection rule. I think it’s worth a try to capture that contrast.
Here’s a try. A selection process winnows down a pool of applicants (let’s call them) to a pool of winners. A step in a selection process, where the steps are applied in a given sequence, is “absolutely negative” if it removes less than half the remaining pool. A step in one process is “more negative” than another step (in the same or another process) if it accepts a larger fraction of the pool.
The concepts of positive and negative selection are not quite well defined in your essay, I think.
Imagine that you have one test, with a gaussian distribution of outcomes. Let’s arbitrarily set a threshold, and if people are above this threshold, they have passed this test. Call the sets of passing A and not passing ~A
Would you call this a positive or negative selection? It is neither, in my opinion.
Now, imagine you have two tests, A and B.
A positive test is one where A U B are selected. A negative test is one where ~(~A ^ ~B) are selected.
In other words—the operative difference between positive and negative selection is OR vs. AND.
Nice step toward clarity, but the leading example contrasts a single-test positive selection rule versus a multiple-test negative selection rule. I think it’s worth a try to capture that contrast.
Here’s a try. A selection process winnows down a pool of applicants (let’s call them) to a pool of winners. A step in a selection process, where the steps are applied in a given sequence, is “absolutely negative” if it removes less than half the remaining pool. A step in one process is “more negative” than another step (in the same or another process) if it accepts a larger fraction of the pool.