re: Homeschool
Ironically, the type of involved parent who would make an ideal homeschooler is also the type of parent that would greatly improve a child's chances in a public school.
When statistics are trotted out showing brilliant home-schooled kids, I have to wonder: would this kid have been equally well-off in a public school, but with the same kind of involved parenting that resulted in the good homeschool results?
Unfortunately, I see no way to statistically test this out, unless you got a set of parents to homeschool one sibling while sending the other one to public school.