Last month, a study by the National Center for Education Statistics reported that private schools consistently outscore public ones, but that their advantage goes away after controlling for differences in student and school characteristics.

In my response to that study, I pointed out that some of the authors’ statistical controls were incorrect and others were misapplied, undermining their conclusion.

Elena Llaudet and Paul Peterson of Harvard University have now run the numbers after correcting for these errors, and the verdict is in: the private school academic advantage is real.

That said, the central point of my earlier blog post remains: the current 10 percent niche of private schools in this country does not constitute a true competitive education industry. Yes, independent schools outpeform government schools, but according to the last International Adult Literacy Survey, nearly a quarter of 16-to-25 year-old Americans are functionally illiterate.

We don’t need a system that’s a little better than this. We need a system that’s a whole lot better. We need real market reform of our entire education sector.