With that kind of "separate specialist school" setup I think you would also need to be careful when analysing outcomes to avoid confounding effects from "the parents are actively interested and engaged in their childrens' education, and have the resources to support it", which I suspect is pretty well correlated with good outcomes.
Don't also forget sampling effects; if you randomly assign children to schools that are of different sizes, the small schools will have higher variance and thus tend to represent both the best and worst items in the set.
And if you _don't_ randomly assign, the effect is even stronger: students who are being well served by the standard/control school don't opt to change, while students who aren't are primed to jump as soon as the option is provided. So the alternative/trial school gets both ends of the bell curve on almost every metric (the main exception being athletic performance, since the larger school typically has more team sport options).
