No, I'm not making a correction (yet). I'd like to draw your attention to this though. The independent in the UK is reporting on the differences in educational results across various schools. The few studies they reference indicate that for a student from wealthy backgrounds, there is little difference in results between those who attend a private school and those who attended a state school. Or even that there is a small benefit to be gained from attending a state school.
I point this out, not to promote state schools over private (though the studies tend to indcate that the extra money the private sector soaks up is wasted). it does demonstrate however, the importance of correcting for as many factors as possible in your work to get at the core, the mechanisms by which the world works. As the author points out, one of the common percpetions is that the school makes a huge difference to educational results. And most people would go, yeah, that makes sense and leave it at that.
What correlates well with the better schools though? Wealth. So the better schools have access to more/better resources/teachers right? Well yes, but at this stage it's correlation only and confusing correlation with causation is an opportunity to visit a world opf statistical hurt. So you do what the authors of the OECD report did and compare children of similar backgrounds at different schools. That way you can tease out whether it is the extra resources that the school has access to or the childs background or the background of the actual child. In this case it looks likely that the background of the child is more important, so it makes more sense to fight against the poverty that children live in than to pump more money into schools (assuming it's an either or proposition). So ideally you'd get a government forming it's policies around important focal points (reducing poverty) with larger effects rather than those with lesser effects (charter schools, increaing class sizes).
What's important though, is that you've looked at that correlation, tested it for causation and corrected your view based on the data that comes back. And if the lesson has been leanrt, then the idea that it's the childs socio economic circumstances that are more important will also be tested.