There's a flaw right in the assumptions here: "(c) the groups of applicants you're looking at have roughly equal distribution of ability." Oh. See, the problem

There's a flaw right in the assumptions here: "(c) the groups of applicants you're looking at have roughly equal distribution of ability." Oh. See, the problem is that if an application process is biased, and applicants perceive that bias, then those against whom it is biased will be dissuaded from applying unless they far exceed the required standards. Whereas those towards whom the process is biased will be more likely to apply, even if they are marginally qualified, because they expect to benefit from the bias. So that means that if you do have a biased process, there's a good chance it doesn't meet criterion c - applicants in the different groups between which its bias discriminates are not equal in ability. So your test might verify a lack of bias, when there is in fact bias present. You can't verify a lack of bias just by looking at the outcomes of successful applicants - you need to look at the outcomes for unsuccessful applicants too, to determine whether your applicant pools really do meet criterion c. Or you could look at the outcomes for nonapplicants, but that's clearly a much harder problem.