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I did some reading & searching but didn't find an answer direct enough to the issue that bothers me: there's something regarding the power of a statistical test, 1 minus beta, that doesn't add up for me. I'd appreciate any assistance, and if it's possible please provide reliable references.

1. It is known that one way to achieve greater power is by using a larger sample size, N.

2. However, an N too large will result in a higher probability to reject the null hypothesis even when there is no effect at all, which is obviously a bad thing.

3. Since a large N also increases the power, one may conclude that a power too large will also be considered as a bad thing.

So, what I'd like to know is whether there is some "recommended upper bound/limit" for the power, one that you shouldn't pass in order to reduce the chances of rejecting the null hypothesis even when there is no effect. Something like the conventional 0.05 for the value of the alpha (in some fields).

Thanks