StATS: Post hoc power is never justified (May 13, 2005).

Someone wrote in and was upset that a referee was insisting on post hoc power for all the outcome measures, and he only wanted to compute post hoc power for the negative outcomes (the outcomes that did not achieve statistical significance).

The references that I cite on my web page about post hoc power are very strongly against using post hoc power for ANY outcome measure. Post hoc power is inversely related to the p-value, so any large p-value is going to automatically have a small post hoc power. For any comparison of two groups, if the p-value is larger than 0.05, the post hoc power has to be smaller than 50%.

If you were silly enough to believe that post hoc power was measuring something useful, you would then have to accept the absurd conclusion that every single negative study that was ever published was underpowered. Certainly, some negative findings occur because the sample size is too small but sometimes they are negative because nothing is going on. Not every treatment being studied is going to be effective, and not every exposure being studied is going to be harmful.

If a referee asks you to include a post hoc power calculation, just say no. Include a sentence in your paper along the lines of

and then cite 2 or 3 of these references.

Apparently I wrote something about this on EDSTAT-L two years ago, and I was quoted on the following web page:

as saying "The best thing to present in the paper is an a priori sample size calculation. If this was not done, rely on the width of the confidence intervals to demonstrate whether the sample size was adequate. A post hoc power computed at a biologically relevant effect size is a poor third choice, and a post hoc power at the observed effect size is pathetic."

Someone interpreted this to mean that post hoc power at a biologically relevant difference is still okay, because it is not pathetic. But it's hardly a ringing endorsement to say that a paper used an approach which could not be characterized as pathetic.

In fairness, most of the criticisms of post hoc power calculations focus on the use of post hoc power at the observed effect size. But you should take a very close look at

because these researchers showed that even a post hoc power at a biologically relevant difference leads to faulty conclusions. They coined a cute acronym, PAP, to describe the faulty conclusions that post hoc power can lead you to.

Further reading:

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Post hoc power