With one gain score, it is possible to use models that control for
observable background characteristics, but those models can not adjust for unobserved student characteristics (such as parental education or student commitment).
The significance of the coefficients on the private - and district - school indicators allows us to test whether there is a statistically significant difference between charter - school parents and parents from either of the other sectors, after adjusting for differences in
the observable background characteristics of the parents they serve.