Noah Smith made a stir with his claim that historians make theories without empirical backing — something I think is a bit of a category error. I mean even if historian's "theories" truly are "it happened in the past, so this can happen again", that the study of history gives us a sense of the available state space of human civilization, then that observation is such a small piece of the available state space as to carry zero probability on its own. You'd have to resort to some kind of historical anthropic principle that the kind of states humans have seen in the past are the more likely ones when you have a range of theoretical outcomes comparable to the string theory landscape . But that claim is so dependent on its assumption it could not rise to the idea of a theory in empirical science.
For example, a common finding in the literature on education production is that children in smaller classes tend to do worse on standardized tests, even after controlling for demographic variables. This apparently perverse finding seems likely to be at least partly due to the fact that struggling children are often grouped into smaller classes.
... we would like students to have similar family backgrounds when they attend schools with grade enrollments of 35–39 and 41–45 [on either side of the 40 students per class cutoff]. One test of this assumption... is to estimate effects in an increasingly narrow range around the kink points; as the interval shrinks, the jump in class size stays the same or perhaps even grows, but the estimates should be subject to less and less omitted variables bias.
|Average class size in the case of a maximum of 40 students versus enrollment.|