There are two studies I keep thinking about. Both involve large numbers of students. Both concern 'sleeper effects' - effects that don't appear straight away, but emerge later.
The first is a study in Boston Massachusetts, and I heard about it via Alison Gopnik. Public preschools had been made available to everyone, but there was such demand that places had to be decided by lottery. Effectively this produced a very large randomised trial, involving more than 4000 students.
But here is the first surprising result. Students of professors who as a group perform well in the initial mathematics course perform significantly worse in the (mandatory) follow-on related math, science, and engineering courses. For math and science courses, academic rank, teaching experience, and terminal degree status of professors are negatively correlated with contemporaneous student achievement, but positively related to follow-on course achievement. That is, students of less experienced instructors who do not possess terminal degrees perform better in the contemporaneous course being taught, but perform worse in the follow-on related courses.
We find that less experienced and less qualified professors produce students who perform significantly better in the contemporaneous course being taught, whereas more experienced and highly qualified professors produce students who perform better in the follow-on related curriculum.