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I'm currently using the multtest package in R, and I am curious to see how the statistical power holds up in a FWER vs. FDR based corrections.

Say for example:

pval <- c(0.018,0.034,0.726)
mt.rawp2adjp(pval,"Bonferroni")
mt.rawp2adjp(pval,"TSBH")

Is there anyway I can get the details of the power of the test retrospectively, using either this package or any other package? Or is what I am asking not making anysense?

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What you are asking doesn't really make sense. Statistical power is a function of your effect size, sample size, and significance criterion. It's a measure of how frequently you'll accept the null hypothesis when you should actually reject it. Power can't be computed from just a list of p-values.

At any rate, it's not really useful to compute the power of your test after you've applied it and gotten p-values. If you find significant p-values, your test was "powerful enough", otherwise, there's either no effect or your test didn't have enough power.

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  • $\begingroup$ The reason I'm after this exercise is that I have read FDR based adjustments preserve the power of the test much more than FWER [1] now before you say that I must use the right tool for the right job, and FWER and FDR are actually asking two different questions etc.. I want to show myself that the FDR correction does indeed preserve more power...or is this something I can not realistically do? [1] Shaffer J.P. (1995) Multiple hypothesis testing, Annual Review of Psychology 46:561-584, $\endgroup$ – Rover Eye Jul 17 '17 at 14:47
  • $\begingroup$ If you have benchmark data where you know what variables actually DO have an effect, you can directly estimate power by calculating how many false negatives you get for each test. $\endgroup$ – Nuclear Wang Jul 17 '17 at 14:50
  • $\begingroup$ If needed, I can use randomly generated normally distributed data, so that shouldn't be a problem. How do I go about doing this? $\endgroup$ – Rover Eye Jul 17 '17 at 14:52
  • $\begingroup$ Power is a useful thing to compute in advance of a study, using hypothetical effect sizes that represent targets of practical interest. Power is not useful to calculate retrospectively; it's an empty exercise, sort of like wondering if you included enough respondents in your pre-election poll after the election is over and the votes are counted. $\endgroup$ – rvl Jul 18 '17 at 2:35

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