Looking at the replies, I do not think the general complaint is that homeschooling is bad for test scores but social development and preparing kids for society outside the house. It definitely requires considerably more, active attention from parents. Perhaps some of these people here have both the time to be hold down a decent career and also tutor their child in multiple curricula that haven't been important to them in decades and ensure that they're maintaining an active social life but I think the difficulty of nailing that as you go-your-own-way is apparent.

Yeah, that study has been debunked or countered by "... among home-educated students applying for college", and the proportion of home schooled kids who apply for college versus those in the traditional education system is far lower, i.e. this is very self-selecting.

They're not more likely to get into college as a whole. In fact, they apply to college a lot less. But in that subset, against public education as a whole, then yes, they do better.

You may want to look wider afield than homeschooling advocacy and lobbyist groups for your stats.