Post-hoc power analysis

Post-hoc power analysis is often criticized for being misleading and useless.

There is a concern that post hoc power analysis might encourage researchers to rationalize non-significant results by claiming insufficient power, even when the study design or methodology were flawed in other ways. This practice can undermine scientific rigor and lead to the publication of inconclusive or misleading findings.
Confidence intervals around effect sizes provide more meaningful insight into uncertainty and the strength of evidence.
If a test yields a non-significant result, a post-hoc power analysis will always indicate low power — but this simply reflects the non-significance and offers no or little additional insight.
Post-hoc power is essentially a reformulation of the P-value. Post-hoc power is a direct function of the observed P-value and effect size.

However, some journals or grant agencies still ask for it, especially if a study yields negative results.

For this reason, we offer the following online post-hoc power calculators.

Literature

Bakker M, van Dijk A, Wicherts JM (2019) The rules of the game in the interpretation of psychological research: Why we should abandon post hoc power analysis. Psychological Methods, 24(4), 492-503.
Button KS, et al. (2013) Power failure: Why small sample size undermines the reliability of neuroscience. Nature Reviews Neuroscience, 14(5), 365-376.
Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.
Gelman A, Carlin JB (2014) Bayesian Data Analysis (3rd ed.). CRC Press.
Hoenig JM, Heisey DM (2001) The abuse of power: The pervasive fallacy of power calculations for data analysis. The American Statistician, 55(1), 19-24.
Lakens D (2022) Practical Meta-Analysis. Sage.
McShane BB, Böckenholt U (2017) The pitfalls of post hoc power analysis. Psychological Science, 28(4), 551-561.