Report power if result is statistically significant We have submitted a paper reporting a statistically significant result.
One reviewer asks us to report what is the power to detect a significant association. As there was a previous paper on this issue, we could use the effect size of that paper to do the calculation.
However, we are surprised by this comment, and would be happy to know what is your opinion and whether you know of references that discuss calculation of power at posteriori when the result is significant.

Thank you very much for your responses.
I should have made clearer that we used a large dataset to run these analyses, so the study is unlikely to be underpowered. However, it involves a complex design, and other than running simulations, there is no simple way to compute power. We are not familiar with simulations to compute power, so I was trying to avoid this :-)

Roughly speaking, observing a significant result in a test with low power means that the observed result is unlikely both under the null hypothesis and under the alternative. So interpreting such a result as evidence in favor of the alternative hypothesis can be problematic.
Now you can say that this is just a wrong interpretation (rejecting the null hypothesis does not mean accepting the alternative), but if there is no evidence in favor of some alternative it's not clear how to interpret the result.
As an extreme example, suppose that someone tries to reject some arbitrary null hypothesis (for example, that there is global warming) by flipping a coin 5 times. If they are lucky enough and observe 5 heads in a row, they can claim that the result is significant ($p < 0.05$) and therefore they reject the null hypothesis. But clearly claiming that global warming doesn't exist based on coin flips is completely meaningless.
The issue here is that such a test has no power (more precisely , the power of the test is equal it's size) - the distribution of the test statistic is exactly the same under both hypotheses.
Notice that in a Bayesian analysis those issues don't exist - in the above case, for example, the posterior probabilities will just be euqal to the prior probabilities of both hypotheses because the test carries no relevant information whatsoever. This is one example of the sometimes problematic aspects of frequentist quantities.
