Rob:
I mean no disrespect, but the issue is the ENTIRE ATTENDANCE area from which private schools can draw—not the school size.
The reason we have A, AA, AAA, AAA is to correct for the draw WITHIN a school.
Again, there is research that private schools have advantages due to the ATTENDANCE area discrepancy, along with the inherent affluence advantage found in most private settings.
The research, which I have posted before:
http://ohiosportsgeography.tadherold.com/hsfoot/publicprivatesxyears/publicprivate.htm
