The data doesn't really say this. Two things to know about education:
- A large percentage of school outcomes are dictated by home life. Interviewing parents or just picking from the population of people who can afford $20k a year allows you to pick from a higher achieving cohort.
- Private schools don't have to provide the same level of services to children who require additional care. This is a significant cost saving. Most schools I've worked at had multiple staff dedicated to the care of just a handful of children.