I'm going to try to throw aside all this emotional content and go at your point, mainly because I think you might learn something here.

Look -- I don't care about immigrants, one way or the other. Statistically, sure, you can make a measurement that has a correlation. Good for you. Lots of measurements and correlations in the world.

To directly answer your question, why would I go about conducting an experiment to show that immigrants are at a disadvantage? To what ends would that serve? What would be the point?

Instead, I might would look at teacher performance, or learning styles, or class size, or school construction, or any one of a million other variables that correlate with immigrants doing a good job. Then I would look for correlation between your immigrant groups and those other variables.

You can pick and choose things to measure and emphasize all day long -- and it doesn't get you anywhere. You want to say that schools are doing a great job and there are factors outside their control that make their outcomes poor in certain circumstances. Fine. I get that. Could be true. Might not be true. Worth exploration.

But the measurement of data and the observation of a correlation is just the initial, total bullshit stage of actually fixing anything. Most of the time correlations don't pan out. Most of the time there are counter-examples to the conclusions you want to reach. Most of the time things change right after you measure them. Most of the time people who don't want/know-how to solve things just sit around making these observations as sort of a chatting class. Most of the time it's nigh impossible to string together any of these correlations into something useful. Something that sounds insightful? Very easy to do. Something that actually has value? Very difficult.

The reality of things is that schools are paid to make a difference, and that there are certain skills that are non-negotiable in our environment. You can add the fact that some schools are doing a very poor job of teaching these skills.

I think those statements are not very provocative.

So, make whatever measurements you want, find whatever correlations you want, build whatever models you want, as long as it further serves the purpose of doing the business of schools: providing an education. If the only purpose is to provide excuses and make ourselves feel better, then it's not really worthwhile. Just go decide you're going to feel that some schools never got a fair shake and be done with it. It's fine with me. It's a perfectly valid point of view to have.

Everything in life is like this, not just schools. You have a job. You do a poor job of it. You either: a) dig down into some data to provide evidence you are not at fault, or b) dig down into some data to start forming models you can test, realizing that the formation of models is only the barest beginnings of anything worthwhile at all. You seem to want to make the measurement, observe the correlation, then announce that it's causal (and then, presumably, go forward to draw some sort of political conclusion)

That's just a bit too far.

How big a factor? How difficult to control? Who knows? Who cares? The point isn't to sit around making observations and bemoaning our ignorance and lack of funds/talent/whatever. The point is that the data is only a very small bit of a solution. We can sit around measuring things and pulling theories out our ass all day long. Not going to help any kids get a better education. The only thing it might do is make us feel better about our preexisting opinions.

I'm not saying that these assertions are false. I simply don't know. All I'm saying is that this type of conversation can go on for a long, long, long time without any useful results. You don't want to do that, either in the real world or with some philosphical school-immigrant problem.