I see two assumptions I made with that. First, that parents more heavily involved are more likely to opt-in to charter schools (or similarly though not equival

I see two assumptions I made with that. First, that parents more heavily involved are more likely to opt-in to charter schools (or similarly though not equivalently, that parents who choose to opt-in are likely to have been more heavily involved). I consider it to be largely self-evident that parents who are not involved are very unlikely to opt-in, and while the converse isn't necessarily true, I think that fact alone would significantly sway the overall correlation of the "non opt-in" population. And second, that being more heavily involved leads to better outcomes for children, which I feel is self-evident, and is also highly supported by a quick google search for 'involved parents better students'.