[ThrustVectoring]

Yeah, compensating factors are a must. If you have a screening function that correlates with both ability to do the job and GPA independently, though, then conditional on passing the screen, the better candidates have a lower GPA. You've essentially got a noisy test for the sum of ability + GPA, so if the sum is high and they have a low GPA, the source of passing the combined test has to come from higher ability.

This process comes up in other similar contexts. SAT scores are not generally correlated between Math and Verbal, but if you screen based off "incoming Freshman to a particular college", an inverse correlation comes up. This is because admittance is based off the sum of the scores - too high and they go to a better college, too low and they get rejected.

[thaumasiotes]

> SAT scores are not generally correlated between Math and Verbal, but if you screen based off "incoming Freshman to a particular college", an inverse correlation comes up. This is because admittance is based off the sum of the scores

Your second point is correct, but your background is wrong; SAT math and verbal scores in the general population are strongly positively correlated, not uncorrelated.

[ThrustVectoring]

Right, lots of tests end up correlated with the general intelligence factor.