<p>
I won’t get into the “could’ve”, but here’s the “should’ve”:</p>
<p>In a school where students are only allowed to take an AP if they have a previous record of academic success in that subject, then the set “students who take APs” is more or less identical to the set “high achievers.” Therefore there’s nothing particularly surprising, or informative, in finding that these students, as a group, continue their high achievement in college. </p>
<p>In order for the results to have the kind of prescriptive meaning you have claimed for them–in order to be able to say, on the basis of this study, “taking APs in high school will improve your performance in college,” you’d have to design a study in which you were comparing apples to apples, i.e., the difference between AP-takers and non-AP-takers with similar academic records before taking the classes. There was some effort to account for this by matching SAT scores, but as we all know, SAT scores correlate very imperfectly with academic achievement.</p>