Clearinghouse method was basically a system where you only count the number of kids that participate in ANY extracurricular activities. This wouldn't be difficult to do...most schools have some form of "Code of Conduct" that students have to sign in order to participate in any extracurricular (sports, band, etc), so the data isn't gonna be hard to grab. This number would be use for classificaiton, not the DOE "enrollement" number. This does a more accurate job of classifying based upon the size of the "participant" population in the school....and it doesn't matter if that school is public, P/P, charter, Hogwarts, etc
The real enrollement disarity the P/P's enjoy is they don't have the (please forgive me for using this term....its the best descriptor, I can think of) "dead weight" part of the student body. They have no mandatory enrollees. ALL public schools have kids they HAVE to enroll by law. These kids may contribute nothing to the school in terms of extracurricular participation (for a variety of reasons), but they are still counted in enrollement.
Now what that percentage of "never gonna participate in anything" enrollee's actually calculates to will vary a LOT.
At Zionsville, Cathedral, University, West Lafayette....its probably a small percentage of the overall student body.
At IPS, South Bend Schools, etc...its probably a LARGE percentage.