Most likely nothing. It depends on what sort of test it is; if it's something non-intuitive like (say) a habit of writing sentences that always have a prime number of words in them, you'll get your false positives but most those people won't pass any other tests, whereas the actual terrorists will.

What Schneier is missing is that while you can't ID people that well from a single test, you can apply a bunch of them. In his example, one test improves the probability of correctly ID a sociopath from 4% to 24%. Apply another, different test of similar efficacy to that result set and you'll have a population of 21 true positives, and 8 or 9 false positives, increasing the probabiliy of a successful ID from 25% to ~70%. Sure, there's no single test that will give you reliable answers, but so what? It's OK to use a multi-pronged solution.