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by noelwelsh 4543 days ago
I agree that the theory says small samples sizes are underpowered. However I believe there are other reasons why small samples over-estimate effects.

We should consider effects as random variables -- different portions of the population will respond in different amounts to the experiment. Smaller samples increase the variance in the measurement of the effect. This wouldn't be a problem if we replicated experiments many times, but we don't, and we only see results of experiments we conduct ourselves or those that are published. Add in the tendency for only significant results to be published and you have a biased sampling of effect size.

As for really small vs small -- I guess I'm used to web experiments, which typically have 1000+ participants.