when variation within each sex is great enough that there are a very large number of one sex who outperform a typical member of the other
That’s not the relevant comparison. In practice the comparison is between an above average members of each sex.
a specific example would be “Females are less likely than males to complete a degree in mathematics; therefore it makes sense to award this scholarship to the equally qualified male instead of the female”.
In your example, than depends on whether the first clause is still true after controlling for whatever qualifications are used in the second.
You don’t always have the luxury of choosing from among a sample that includes above-median performers.
The second case is a textbook example of sexist thought; I thought it was clear that the first clause was not controlling for anything, while the second was making a specific measurement of expected performance.
You don’t always have the luxury of choosing from among a sample that includes above-median performers.
In that case comparing average members of one sex with the above average members of the other is still not the right comparison to make.
I thought it was clear that the first clause was not controlling for anything, while the second was making a specific measurement of expected performance.
Even this statement is ambiguous. Does the specific measure of expected performance actually screen of gender?
That’s not the relevant comparison. In practice the comparison is between an above average members of each sex.
In your example, than depends on whether the first clause is still true after controlling for whatever qualifications are used in the second.
You don’t always have the luxury of choosing from among a sample that includes above-median performers.
The second case is a textbook example of sexist thought; I thought it was clear that the first clause was not controlling for anything, while the second was making a specific measurement of expected performance.
In that case comparing average members of one sex with the above average members of the other is still not the right comparison to make.
Even this statement is ambiguous. Does the specific measure of expected performance actually screen of gender?
You never need to compare the average, because you only ever need to compare a small number of individuals.
Performance in the production environment correlates with the measured expectation equally well for males and females.