Knowledge base Updated 2 November 2026 1 views

Effect Size

A quantitative measure of the magnitude of a phenomenon, independent of sample size. It answers how big, where a significance test answers only whether an effect can be distinguished from zero.

Definition

Common standardised measures:

Cohen's d: mean difference divided by a standard deviation. Hedges' g applies a small-sample correction and should be preferred below roughly 20 per group.
Pearson's r: standardised linear association.
Odds ratio and risk ratio for binary outcomes.
Eta squared and omega squared for variance explained; omega squared is less biased.

Cohen's small, medium and large labels — .2, .5, .8 for d — were offered as a fallback for planning where nothing better was available. Cohen said so explicitly. They have become a scoring rubric, which is not what they are for.

Unstandardised effect sizes are often more useful when the measure has a meaningful scale: three fewer symptoms, four points on a known instrument, two hours of sleep.

History

Effect sizes were formalised for meta-analysis, and Glass, Smith and later Hedges built the machinery in the 1970s and 1980s.

Cohen's advocacy for reporting them predates that and was mostly ignored until journals began requiring it, which for most of psychology was after 2000.

Theory

Standardisation makes measures comparable across instruments, which is what meta-analysis needs, but it does so by dividing by a standard deviation — and that makes the value depend on the variability of the sample.

The same true difference produces a larger d in a homogeneous sample than in a heterogeneous one. A restricted-range clinical sample and a general-population sample can report very different effect sizes for an identical underlying effect. This is why comparing standardised effect sizes across very different populations is treacherous.

Within-subject designs raise a further problem: d computed with the difference-score standard deviation is not comparable with d computed with the raw standard deviation, and papers frequently do not say which was used.

Research

Typical effect sizes in psychology are smaller than the conventions suggest. Analyses of large samples of published effects place the median r around .20 or below, so a medium effect is not typical.

Published effect sizes are inflated by publication bias and by low power, so the literature average overstates reality. Comparisons of preregistered with conventional studies find smaller effects in the former.

Confidence intervals around effect sizes are wide in typical studies and are often omitted, which conceals how little a single study establishes.

Applications

Sample size planning, meta-analysis, comparing interventions, and translating research into practice.

For clinical work the important question is whether the effect is large enough to matter to a person, which is a question about the minimal clinically important difference on the actual scale, not about whether d exceeds .5.

When reporting: give the effect size with a confidence interval, state which standardiser was used, and give the unstandardised value where the units mean anything.

Criticism

The small/medium/large labels are misused constantly and were never intended as benchmarks.
Standardised measures depend on sample variability and so are not as comparable as they look.
Statistical magnitude is not practical importance. A small effect on a population-wide intervention may matter enormously; a large effect on a proxy outcome may matter not at all.
Reporting is inconsistent, especially for within-subject and multilevel designs, where several defensible definitions coexist and are rarely specified.
Effect size does not fix a bad design. A precisely estimated effect from a confounded study is a precisely estimated confound.

References

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Erlbaum.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science. Frontiers in Psychology, 4, 863.
Funder, D. C., & Ozer, D. J. (2019). Evaluating effect size in psychological research. Advances in Methods and Practices in Psychological Science, 2(2), 156-168.
Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size. Journal of Educational Statistics, 6(2), 107-128.

Written for PsychologyOrbit and reviewed before publishing. It is a summary for professionals and students, not clinical guidance, and it is not a substitute for the primary sources listed above.