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I am conducting a regression analysis on TNF-a in relation to a genetic marker. I performed a post-hoc power calculation using a software called Quanto. The mean(SD) of my outcome variable is 34(14). The Minor Allele Frequency of the genetic marker is 0.102. The Beta coefficient of the predictor from the regression model is 2.852 and my sample size is 799

The power calculation result shows that the minimum detectable effect size (Beta) for a sample size of 781 is 3.271, while the observed effect size (Beta) from the regression model is 2.852. What can I conclude from these results? If the observed effect size is lower than the expected effect size, does it mean that the study is underpowered?

arshad
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    You can conclude no more than what is presented from the regression. Postbox power has been discussed extensively here and elsewhere, and the conclusion is your energy is best spent elsewhere. – Demetri Pananos Apr 10 '23 at 22:04
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    I am not very experienced in stat. If you can help me with a reference, will be great – arshad Apr 10 '23 at 22:22
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    Since you are modeling the outcome as random, why would you be at all surprised or concerned to observe an outcome that varies a little bit below or above what you expected? Nature doesn't suspend the laws of probability just because you were foresighted enough to do a power analysis beforehand! – whuber Apr 10 '23 at 23:13
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    @arshad see this answer https://stats.stackexchange.com/questions/384011/power-analysis-for-logistic-regression-with-dummy-independent-variables/384013#384013 – Demetri Pananos Apr 10 '23 at 23:48
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    Consider that a sample mean with a different value from a hypothesized population mean doesn't necessarily imply that the hypothesized mean was wrong (it may be due to sampling variation). So it is here - except your calculation using a prior effect size doesn't need to have been an accurate description of the actual situation -- if the power calculation was about finding the sample size to attain a particular power if that was the effect size, this property may be desirable whether or not that was really the effect size. – Glen_b Apr 11 '23 at 00:46

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