From Aleks Jakulin:
"I do know that I get anxious whenever a correlation analysis tries to look like a causal analysis. A frequent scenario introduces an outcome (test performance) with a highly correlated predictor (say poverty), and suggests that reducing poverty will improve the outcome. The problem is that poverty is correlated with a number of other predictors."
I think that the dense correlation is precisely the point that makes inference challenging here. I like to point out California as being a good example of a puzzling outlier in the original study. There is no a priori reason to expect that California would do as poorly as it does relative to other states. But different groups have different explanations.
One hypothesis is that "teacher tenure" leaves weak performers in the classroom for decades. This seems to be the position of people like Michelle Rhee.
Another hypothesis is low educational spending in the state. According to wikipedia, "In teaching staff expenditure per pupil, California ranked 49th of 51".
A third hypothesis is the composition of people in California just leads to lower educational performance (due to innate differences with, for example, the population of New York state).
I kind of suspect the second hypothesis as most likely, but, given how inter-related things are it is unclear how you would do inference here. And some forms of the first hypothesis would lead to policies that could make things worse if the second were true. The third would suggest no policy is likely to make an important difference.
Coming up with clever ways to distinguish between these hypotheses is not trivial.
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