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Vaniver comments on Too good to be true - Less Wrong
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Another way of asking my question, perhaps more clearly, is: how do we know if the 60 considered studies were testing the hypothesis that there was a link or the hypothesis that there was not a link?
I think the answer to this is "because they're using NHST." They say "we couldn't detect an effect at the level that random chance would give us 5% of the time, thus we are rather confident there is no effect." But that we don't see our 5% false positives suggests that something about the system is odd.
OK, that sounds straightforward.
How does one know that the 60 studies are these? (rather then the others (e.g., that were designed to show an effect with 95% probability, but failed to do so and thus got a negative result)).