[Retric]

Boarding schools exist, as do affluent areas next to poor ones.

Anyway, there are several ways to compare systems, some private schools operate in whole or in part on a lottery system so you can track students who do or don’t get in. But the most common method is to model parent education and income as a predictor of performance and then compare outcomes.

As you suggest poor students are underrepresented in private schools, but some do get in. The important thing to remember is a student who received a scholarship isn’t representative of the general population.