For example, if X and Y are linearly correlated at .8, are there something like confidence intervals I can put on the classification rate obtained when threshholding X to identify Y > k?
The motivation for the question comes from lots of research in the social sciences (particularly education research), where a high correlation is presented as evidence of a strong relationship. But many of the problems under consideration are best thought of as classification problems (e.g. does SAT predict college freshman grade of B+ or better? or Will Tatiana drop out of school?). So it's quite possible to have a 'strong' research result that's essentially meaningless unless there's an implication from correlation to classification.
A discussion of SAT as classifier can be found in my blog post here.
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