Post-hoc power analysis for null results: how to use 95% confidence interval instead? My PI is having me run a post-hoc power analysis on our samples, with a treatment and control group and a binary outcome. I was using this website to start the process. However, at the end, the website cautions:

The Dangers of Post-Hoc Analysis
Post-hoc power analysis has been criticized as a means of interpreting
negative study results.2 Because post-hoc analyses are typically only
calculated on negative trials (p ≥ 0.05), such an analysis will
produce a low post-hoc power result, which may be misinterpreted as
the trial having inadequate power.
As an alternative to post-hoc power, analysis of the width and
magnitude of the 95% confidence interval (95% CI) may be a more
appropriate method of determining statistical power.

What does this mean? How would I use the width of the CI to determine if the statistical power was adequate? Is there a common threshold that I should consider?

If your CIs are narrow, then you have an idea of how large the effect is, and you can say with some confidence that the effect is small, and that's why you didn't detect it.
If the CIs are wide, then you don't know how big the effect is. Maybe it's big and you didn't detect it because you didn't have enough power. Maybe it's small and you didn't detect it because it's small.
