Empricial evidence would be nice but isn't really necessary.
Intuitively, do you think home-schoolers are better off or worse off than their factory-school counterparts in these areas (to pick a few off the top of my head):
- drug use?
- promiscuity?
- pre-marital pregnancy?
- STDs?
- communication skills with all age groups?
- critical thinking skills?
- independence in thought?
- courage of convictions?
- freedom from hazing?
I'd say it's up to the factory schools to prove their kids are on average better off than the home-schoolers, not vice-versa. I don't think they can.