Also, I'd mention that, even if, say, you have a noisy (presumably cheap) test that you give to everyone, and then you give an absolutely perfect (presumably ex

Also, I'd mention that, even if, say, you have a noisy (presumably cheap) test that you give to everyone, and then you give an absolutely perfect (presumably expensive) test to minorities that fail the first test... It's probably the case that, of the people who failed the first test due to noise but would pass the second test, most of them are just barely above the "passing" bar. Because it seems reasonable to guess that people way above the bar have a smaller chance of failing the noisy test than people just barely above the bar. The policy would then lower the average ability level for hired minorities (though it wouldn't bring it below the "bar"). How large this effect is depends on just how noisy the first test is and on how widely above the bar people's abilities range.