NY Times article- School Vouchers might not be a great thing after all.

[roethlisburger]

Also, private school students do show a self-selection bias in that the student and/or parents care enough to choose the private school, while public schools have some students attending by default where the student and parents care little about education.

All good schools, including public ones, have selection bias. This can be direct, as in the case of public magnets, or indirectly through parents who have the means and motivation to move to areas with the best public schools.