Homeschooling by the Numbers
My dh found an interesting "infographic" about homeschooling statistics. Click the image to enlarge.
Math Mammoth video review
Here's a new Math Mammoth video review posted on Youtube. (It does cover some other elementary math programs also.)
Comments
1) homeschoolers don't have to take the SAT, so there is an enormous self-selection bias, with only the better-prepared students choosing to take the exam.
2) the demographics of the three populations are not matched. The effect that is being observed may be due entirely to the education level and income level of the parents, and have nothing to do with the education method.
The evidence is that the biggest determinant of outcomes for public school students is the value their parents place on education. Parents who care a lot about their children's education tend to do better in whatever educational setting they attend.
Clearly parents who homeschool place a high value on their children's education, and thus one would expect them to do better in general.
As for point #1), nobody has to take the SAT (homeschooled or otherwise), so the self-selection bias is not confined to homeschoolers.
Alaska subsidized homeschooolers through it's government-operated correspondence schools. Students in these schools take standardized tests and perform as the statistics above indicate. Aggregate State-level NAEP statistics suggest that this is not sample bias induced by self-selection, since Alaska has (had, last I looked) the highest 90th percentile score (NAEP 8th grade Math) of all US States.