to be fair, other schools (except Cornell) don't have explicit engineering schools, with the self-selected applicant pools that come along with them. it's not disingenuous to compare admit rates across the liberal-arts colleges.
Well, the only schools you can compare CC directly to are Penn and Cornell CAS. (Penn also has a distinct engineering school if I'm not mistaken).
The other 5 ivies (particularly the ones in question here, HYP) have engineering programs, but they're all rolled into "the college" at the respective university. So if you're going to do a head to head with HPY, you have to use the combined statistics.
Also, though, you'd have to consider that Columbia has significantly more engineering students than HYP, Brown, Dartmouth, etc. So whereas HYP's higher engineering acceptance rates don't make a huge impact on acceptance rate, Columbia's number does.
Apples to apples then? We should go department by department and normalize across all schools to account for discipline differential between the humanities, social sciences, and natural sciences between the schools.
You just can't do it.
In terms of comparing school to school, the only numbers that matter are what it takes to become an undergraduate at said school. Of course there's a whole 'nother can of worms here (GS).
except you don't apply for specific majors in the us. they do that in the uk system, and compare rates like you described.
the thing with engineering schools is that applicants tend to self select, so they distort the numbers that show "what it takes to become an undergraduate". this doesn't happen so much at cas (except chicago) which is why the value of that rate is more consistent across schools.
Leaving HY aside, in order to get a meaningful comparison against P, which not only has over 150 engineering majors a year, but is considered a better engineering school than Columbia, you'd need to use the combined rate, correct? But then you'd use a different rate against HY? Does P use a different rate against HY?