Your claim is not true. If you factor out the most significant variable, some other variable becomes the most significant one.

Yeah, maybe more expensive teachers, for example.

Or more talented kids.

Richer or more connected parents maybe

> there would be no significant difference between the students in the study

I didn't say this. I say that you can't generalise to students NOT in the study, i.e. students with parents who didn't care to participate in the lottery.

Of course you can. You can control for the factor/variable you said was the "single most important", which is done through the design of the study, by your own admission. And then look at results from the other factors.

Whether your factor is important or not doesn't even enter the picture.

Just because something is the most important condition doesn't make it the only important condition.

But it makes it the most significant condition. It was in the stated initial premise.

And if they're all important (according to GPs list) then maybe more expensive teachers, better properties/real estate, supplies, etc is important enough anyways.

> > Having engaged parents is the single most important condition for getting a good education.

> If that was true then there would be no significant difference between the students in the study, since all of them had engaged parents.

This does not follow. Just because something is the most significant condition doesn't mean that two things meeting that condition will have no significant differences.

EDIT: For example, let's say breathing is the single most important thing to do in order to stay alive. That doesn't mean eating isn't important to do as well. If two people breathe, but only one of them eats, they will have significant differences in outcome even though they both met the single most important condition.

Sure, but OP ranked them specifically to downplay the effect of teachers (and other factors caused by wealth).

You can't have it both ways.

Either engaged parents is significantly more important, or the other factors are still very important.

And this discussion is entirely sidestepping the fact that OPs list is entirely arbitrary.

I think this is pretty simple and folks are talking over each other.

Involved parenting is a blocker issue, not just a critical one. There may be other critical issues in the queue, but those are blocked on that first one.

So the other issues being resolved may not matter at all if the first isn't completed first.

That's more or less how I see GPs argument. My rather diverse education background certainly lets me see that hypothesis as absolutely true - but I have my own personal biases due to experiences.