<p>Probably should emphasize the difference between the actual meaning of correlation and the more colloquial meaning of it. Given the fact that people aren’t randomly assigned to medical schools there is probably a greater than 95% chance that some 0<r<1 correlation between prestige of medical school and competitive residencies exists. It’s really not a stretch to assert that schools which recruit the top students are more likely to have students that go on to top residencies than the schools that don’t recruit the top students.</p>
<p>None of that contradicts the rest of your post though jug, which I do agree with.</p>