A <em>d</em> = 0.80 is called a "large effect" and sounds enormous. Translated: the average treated person outscores 79 % of the control group, and the two distributions still <strong>overlap by 69 %</strong>. That is the sentence the discussion needs, and almost nobody writes it.
U₃ = Φ(d) · PS = Φ(d/√2) · overlap = 2·Φ(−|d|/2)
Cohen proposed his benchmarks (.20, .50, .80) as provisional references "in the absence of better", and explicitly warned against using them as a universal scale. They have been used as a universal scale for forty years.
The problem is not that they are imprecise: it is that they mean nothing to a reader. "Large effect" does not say how many people it happens to, how far apart the groups are, or whether the intervention helps anyone in particular.
The three translations above do say that, and they cost nothing: they come out of the same d you already have.
U₃ in the discussion. "The average treated participant reached the 79th percentile of the control group" is a sentence anyone understands and anyone can check.
Probability of superiority with a clinician. It answers the question they actually ask: if I take two patients, one from each group, how likely is the treated one to do better? At d = 0.80 the answer is 71 %, not 100 %.
Overlap when an effect is being oversold. It is the number that brings the conversation back to earth: a large effect still leaves the two distributions overlapping by two thirds.
All three formulas assume normality and equal variance in both groups. With skewed distributions — reaction times, relapse counts, anything with a floor at zero — they stop being faithful.
When that happens there is an alternative that assumes nothing: the common language effect size computed directly on the data, counting in what share of all possible pairs the treated group wins. It estimates exactly what PS estimates, without assuming a shape.
And there is one case where none of this works: when the treatment changes the variance rather than the mean. Both distributions then share a center, the effect is real, and d reports it as zero.
All thirteen effect size conversions, grouped by what each one is for, are in the index.
If you use it in your thesis or in a paper, cite it so that readers of your Methods section know how the calculation was done.
Ciudad-Fernández, V. (2026). Cohen's d to overlap converter [Web application]. Ciudad Science. Retrieved October 14, 2026, from https://analisisdedatospsicologia.com/en/convert/cohens-d-to-overlap
For your Methods section: Cohen's d was translated into distribution overlap and probability of superiority, assuming normality, using the Ciudad Science cohen's d to overlap converter (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026convdaporcentajedesolapamiento,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{Cohen's d to overlap converter}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/convert/cohens-d-to-overlap},
urldate = {2026-10-14},
note = {Accessed 2026-10-14},
}Yes, and it usually improves the abstract. What you should not do is replace d with U₃: d is the metric that lets your study be compared and meta-analyzed. U₃ accompanies it, it does not replace it.
Yes: under normality, probability of superiority equals the area under the ROC curve separating the two groups. Same number, told two ways.
Overlap uses the absolute value, so it does not change. U₃ and probability of superiority flip: at d = −0.80, the average treated person sits at the 21st percentile of the control group.
There is no threshold, and that is the point. What is useful is showing it: d = 0.20 overlaps 92 %, d = 0.50 overlaps 80 %, d = 0.80 overlaps 69 %, and d = 2.0 still overlaps 32 %. Almost no psychological intervention truly separates the distributions.