How would a study of forced homeschooling go?

One thing missing from all the data of homeschooling, are apathetic parents.  I sometimes hear in political discussions how homeschooling is "all well and good for you people, but most parents would never teach their own".  And I have my suspicions, but I would love for a real large scale study with control and everything to look into it.

If we could take a group of parents who are currently in public school and divide them into three groups.

Group one, nothing interesting, have them carry on as usual in public school as a control group.  (though using the whole rest of the nation as a control group aught to work.)

Group two - insist they homeschool.  Not folk who want to homeschool already, but folk who signed a guarantee agreement to educate their kids the way the study says, and the study says they are in charge.  I don't think any particular brand of homeschooling matters, just that the parents are now in charge.  Of course provide links to local support -or at least a suggestion that they use the internet to find info. (it would be easier to get good results if the study were done in a city like Charlotte with lots of homeschool support, but for accurate results I think a random sampling of cities would be better)

Group three - Insist the parents volunteer at the school, be active in homework, and participate in the education of their children just as much as a homeschooler would have to (like good parents already do really).

Sadly the only way to compare the groups would be tests, though I think a psyche test in addition to academic tests would be a good idea.

In the end, I am sure group one would fare the worst, but of group two and three, those are the results I am curious about, is it really just as good for a parent to be active as it is to homeschool?  Of course I believe homeschooling is better (or at least easier on me), but I don't see hard scientific evidence to prove that.

Would it be better to take parents of newborns so that they know from day one how they are going to school?  Or maybe age 3 or 4.  Or maybe highschool......

Or maybe it would be better to do highschool only the KID has to take responsibility for their own education.  Which really by the teen years a kid aught to try and do.