We have posts on here discussing why post hoc power calculations are flawed.
What about post hoc calculations of the effect size that we could catch? That seems logically equivalent. If we are not supposed to calculate the power to detect an effect of $1$, then we should not calculate the effect we can detect with $80\%$ power.
(Perhaps this warrants a separate question, but sample size and $\alpha$-level also play into the equation. Is it invalid to do a post hoc calculation of the sample size or $\alpha$? (I am thinking of how R's
pwr package will calculate one if you give the others, something like what I posted when I first joined Cross Validated.) But I mostly want to talk about post hoc calculations of effect size.)
We have observations from two groups and perform a t-test of their means that gives $p=0.1626$: insignificant at $\alpha=0.05$.
We want to declare equivalence of the groups, but the SMEs are unsure how small of an effect size warrants equivalence. "Tell us what kind of effect you can detect," they tell me. "We'll come back and say if that effect is important."
I know that we like to operate with the standards of $\alpha=0.05$ and a power of $80\%$, so I use the sample sizes, $\alpha$-level, power, and observed variances to calculate the effect size I can detect. I tell the SMEs, "We can detect an effect size of $0.25$."
If I were to flip the problem around to have an effect size of interest, say $0.3$, and calculate that we have $90\%$ power to detect such a difference, that seems like an invalid post hoc power calculation. It seems like the post hoc effect size calculation is just as invalid.
Really, it comes from a paper by Rebecca A. Betensky: "The p-Value Requires Context, Not a Threshold". She shows what to do if we declare an effect size of interest. I can imagine her method being turned around to have me answering what kind of effect we can detect.