Makes sense to me. A random-effects is essentially a multilevel model, and you'd expect correct modeling of such heterogeneity to increase rather than decrease power.
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Maybe do some simulations to confirm.
End of conversation
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Kahneman talks about the "law of small numbers" in Thinking, fast and slow. Small samples are more extreme/less representative than large samples. I could see getting more extreme t-stats from smaller samples. Not sure if relevant
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Sounds like bootstrap?
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