I don't know if comparing charter schools to regular schools is fair, when I think their may be a significant difference in the population of the school. Or at least I don't know that there isn't.

Even with a lottery, you have a bias towards students with parents that enter the lottery. People with caretakers that are less concerned about their well-being probably are less likely to be entered in the lottery.

You should really compare students who attempted to get into a charter school vs those that didn't.

If you want to show evidence of charter school success that's definitive, you would need a randomized controlled trial. split a school district into half charter schools half public schools. And you wouldn't let the charter schools kick out students who underperform or have behavior problems, or otherwise make sure that such students don't skew the charter school's metrics. See what happens.

I guess I'm not sure how much the success of a student population can be attributed to teaching methods, and how much to aspects of the child's life. We all know that wealth has dramatic effect at college attendance and graduate rates for those that attend college.