Meaning of low power in neuroscience after combining results of many meta-analyses (Button et al 2013) In a 2013 review article in Nature Neuroscience, Button et al. Power failure: why small sample size undermines the reliability of neuroscience, it was stated that:

the average statistical power of studies in the neurosciences is
  very low

They searched for meta-analyses, calculated the post-hoc power in each one of them, and combined the results by taking the median post-hoc power. The median was 20%. I just don't get it. Post-hoc power is always inherently associated with the achieved p-values. Isn't it the same as to write that median p-value was something like ~0.3 which corresponds to the post-hoc power of 20%?
So basically how does this result undermine the quality of research in neurosciences? It seems that they have been publishing studies with a lot of non-significant p-values.
This review is a Nature Neuroscience study with very famous authors, so I think my interpretation is more likely flawed.
EDIT: I would see some point if they included only studies with nominal significance. In that case the median power would tell the median replication probability of significant findings.
 A: I'm not familiar with this particular study but am familiar with estimating the power of an area of research using a meta-analysis. Your statement that "post hoc power is always inherently associated to the achieved p-values" suggests to me that you are assuming that the post hoc power for each individual study contributing to a single meta-analysis is based on the assumption that the observed effect equals the true population effect. Only with that assumption will the post hoc power be related to the p-value (I personally find this form of post hoc power analysis to be pointless, but that is a bit off topic). 
What I believe the authors of this paper are doing, given that it is what is typically done, is to assume that the meta-analytic mean is the true population effect and to estimate power for the studies contributing to that mean using that value, not each study's observed effect. Thus, the mean power within a meta-analysis is a function of the overall meta-analytic mean effect and the sample sizes (or standard errors) of the individual studies. They did this for each meta-analysis and computed the median power across them. 
