Uh, yes, of course. The assertion that the set of homeschooled children is self-selected doesn't have to mean that the kids themselves made the choice to be part of the set. Their parents made it. As I suspected, you really don't understand the concept.
Your assertion is that the Christian element of those homeschoolers' education is a significant factor. You can't demonstrate that without controlling for other factors, such as the influence of "parent...who care about the education of their children to the point of being heavily personally involved."
As I suspected, you’re arrogant and believe you are more intelligent than others because of your worldview (EVERY lib thinks this way).
SO WHAT if the parents selected it?
Are you asserting that ONLY THE PARENTS OF THE SMART KIDS choose homeschooling? Nonsense.
You have not adequately proven that homeschoolers are a “self selecting set” that explains away significant differences in academic achievement and understanding of science.
Yes, the Christian element DOES factor in because when you’re teaching from the Truth instead of from a basis of error, you can’t help but have more correct outcomes.
I see that, in your last sentence, you do agree that the homeschooling system IS superior. We can agree on that.