<p>You can’t simply look at raw quantities. Princeton is smaller than Harvard, Stanford,… You can’t even consider just percentages on their own since you can’t assume Princeton and say, Stanford (purely hypothetical example) attract the same percentage of pre-meds. It would be like saying Caltech isn’t that great because they (probably, taking a guess here) have so many fewer med school matriculants than Harvard. Never mind that Caltech has an entering class of less than 250 each year and typically attracts techies… If you wanted to do a thorough analysis, you’d have to actually look at lots of information that isn’t readily available and try to estimate the treatment effect (nearest-neighbor matching comes to mind but I’m not an econometrician).</p>