Why Observed Power Cannot Explain a Non-Significant Result
Observed power largely restates the p value. Use effect estimates, confidence intervals and prospective planning after a non-significant result.
What is observed power?
Post-hoc power is calculated after data collection using the observed effect and standard error. Under common tests and a fixed alpha, it is nearly a one-to-one transformation of the p value: non-significant results produce low observed power and significant results produce high power. It adds little new evidence.
The circular argument
“p=0.12 and power was 40%, therefore the sample was inadequate” is circular. Low observed power does not explain the result. The observed effect is also unstable in small samples, making the calculated power unstable.
Use these instead
Effect estimate and 95% confidence interval
Comparison with clinically important values
Prospective sample-size assumptions and actual recruitment
Model diagnostics and data quality
A new prospective calculation for a future study
A wide confidence interval directly shows which effects remain compatible with the data. This is more informative than relabelling the p value as power.
References
Interpretation of Statistical Power after Data Collection. 2020.
Greenland S et al. Statistical tests, P values, confidence intervals, and power. 2016.
Accessed 20 June 2026.