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Excuse my ignorance. I tried to look up the questions but couldn't find it. I had a discussion today whether it is possible that a study result will have a p<0.05 yet that would be caused by chance (i.e. a possible underpowered study - if I got all the terms correctly). My thoughts were that if there is a statistically significant difference (proven by p=0.03) then the study is automatically powered enough to detect that difference.

Thank you!

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The power of a test depends on the sample size and the alternative hypothesis under consideration. It is not affected by whether or not the null hypothesis is rejected. If a study is highly powered the chance of rejecting the null hypothesis when the alternative is true is greater than for a study with lower power but the null hypothesis can be rejected by chance when it in fact holds and it also can be rejected when the alternative is true and the study is not highly powered.

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