<p>Re the preceding question, here is a partial explanation (I think):</p>
<p>A school’s acceptance rate is lower if it is very well known and gets a lot of applications, some of which come from people who are not especially well qualified but apply because they have heard of it and think it might somehow work out for them. So that school may have a 20 percent acceptance rate while another school has a 40 percent acceptance rate. That does not necessarily make the first school more selective, because the second school may have an already self-selected pool of applicants; thus there are perhaps just as many highly qualified students to choose from. So the overall percentage of acceptances will vary a lot, but number of serious applicants may not be as different as the percentage implies, and the second school may be accepting as highly qualified a group as the first school and being just as careful about who it admits. The Chicago/Columbia example used by another poster seems like a good illustration.</p>