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torekp comments on [Retracted] Simpson's paradox strikes again: there is no great stagnation? - Less Wrong Discussion
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One heuristic I try to use in making sense of claims about broken-down data is to zoom out to the big picture for a "reality check." [/tongueincheek] Reality doesn't play favorites with big versus small pictures.
That isn't a bad heuristic either! However in practice the aggregate claims about scores are often used to make an argument relying upon internal homogeneity, and I don't see the corresponding "scores are up among all groups so aggregate scores must be higher" often, which would require more information and space.