Source? Back-up data, please.
Your assertion that homeschooled kids do not perform as well as publicly educated kids with "parental involvement" was challenged. Since it has been two days since I challenged that statement without a response, I and anyone else reading this thread can safely tuck your unfounded assertion into the appropriate file.
The "Flatulence Passed Around The Teachers Lounge Between Reading 'Heather Has Two Mommies' To 8 Year Olds" file.
And just how would one design a study measuring "parental involvement" in some relevant sense? I suppose it would be possible, but the methodological problems and cost would be formidable (basing a study on self-reporting of "involvement" by parents would be absurd. As Ann Coulter illustrated the problem, in her survey of the sexual activity of teenage boys 90% reported that they were having sex every night, 60% with Pam Anderson).
The NEA and ed school people publish garbage, which gets headlines, and then the work is shown to be essentially fraudulent, which doesn't get headlines. See my prior post on the NCES massaging of NAEP data vis private schools.