The education reform movement relies heavily on anecdotes of remarkable, odds-beating schools, but when you take a close look at those schools that had significantly superior performance, some if not most of the difference in scores could be explained by selection and peer effects.
This isn't to say these schools weren't benefiting their students. Regardless of the reason, these kids were better off. Nor is this to say that these schools weren't doing something right. I can tell you that many are well-run and highly innovative.
But even taking all of that into account, selection and peer effects are huge and can swamp almost any other factor you can think of. These effects are seldom if ever adequately accounted for (And before anyone says the word 'lottery,' please take a look at this). This makes it all but impossible to accurately measure the impact of these schools but people like Jonathan Chait continue to cite them without any caveats.
I came across a segment of This American Life that beautifully captured my feelings on the subject. Just play the clip below and every time you hear 'heroin,' substitute in 'selection and peer effects' (you can just ignore the parts about crystal meth and pancakes).
From Kumail Nanjiani:
So remember, selection and peer effects are doing the heavy lifting.