So, I'm actually a biologist trying to wrap my head around the idea of power of analysis to help design an experiment with the proper sample size. I understand that power of analysis is used to help avoid type II errors, but I came across this paper:
which seems to say (if I'm not mistaken) that in underpowered studies, you also increase your risk for false positives. The other thing that confuses me, is that if you keep adding more samples to increase your power, of course you make any finding statistically significant, even if your effect is small. Is there some sort of balance between power and number of samples so that one avoids the pitfalls of an underpowered experiment, and also an overpowered experiment where the results will produce a statically significant result that might not be interesting because the effect size is so small?