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John_Maxwell_IV comments on [Link] Personality change key to improving wellbeing - Less Wrong Discussion
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My thinking is that if two factors are correlated in some data, and it's not a fluke/fraud/coincidence/etc., it's reasonable to conclude that at least one of these three is true:
In other words, if you can only think of one plausible explanation for a correlation, it's reasonable to assign it a lot of probability mass (in the same way that if you can think of only one plausible explanation for a murder, it's reasonable to assign it a lot of probability mass). Of course, it's important to keep in mind unknown unknowns, things you didn't think of, and all of the improbable scenarios that might add up to a lot of probability.
These often aren't exhaustive. There's the example of a prestigious university that only admits students who are exceptional either academically or musically. Among students at that university, academic ability is negatively correlated with musical ability, since either one is enough to be admitted, but it is rare to be exceptional in both, assuming they are uncorrelated in the general population. This does not fit into any of those three common reasons for correlation.
That's a good scenario to think about. So maybe we can add an additional case where there's some filtering process that's affecting the data we see.
A similar, possibly more politically fraught example is the university that grants scholarships either on the basis of academic merit or financial need.