Effect Size

Effect size is a standardized, quantitative measure of the magnitude of a difference, relationship, or association observed in a study, reported independently of sample size and distinct from statistical significance. Where a p-value indicates only whether an observed effect is unlikely to be due to chance, an effect size (e.g., Cohen's d, Pearson's r, an odds ratio) indicates how large or practically meaningful that effect actually is. The APA Publication Manual (7th edition, Section 6.5) requires reporting an effect size and confidence interval for each primary outcome, and most major journals across the behavioral, social, and biomedical sciences hold manuscripts to an equivalent expectation.

ByCASRAI Editorial Board

· Last updated 23 Jul 2026

Worked examples

Is an instance

A manuscript reporting t(98) = 2.85, p = .005, d = 0.57 is reporting both statistical significance (p = .005) and effect size (Cohen's d = 0.57, a medium-to-large standardized mean difference by Cohen's conventional benchmarks) — the two numbers answer different questions and neither substitutes for the other.

Is an instance

A correlational study reporting r = .42 between two continuous variables is reporting Pearson's r as both the strength/direction of the association and its own effect size — no separate effect-size conversion is needed because r is already standardized.

Is an instance

A case-control study reporting an odds ratio of 2.3 (95% CI 1.4–3.8) for an exposure-outcome association is reporting effect size for a binary outcome; unlike Cohen's d, an odds ratio's confidence interval must be read against 1 (no effect), not 0.

Looks similar, but isn't

Not an instance

A manuscript stating "the treatment group significantly outperformed control (p < .001)" with no effect size or confidence interval reported has established statistical significance but told the reader nothing about the magnitude of the difference — current reporting standards (APA, CONSORT-aligned checklists) treat this as incomplete Results reporting regardless of how small the p-value is.

Why effect size is a manuscript-reporting requirement, not just a statistics topic

Effect size is a standardized, quantitative measure of the magnitude of a difference, relationship, or association observed in a study — reported independently of sample size and distinct from statistical significance. A p-value only tells a reader whether an observed result is unlikely to have arisen by chance; it says nothing about how large or practically meaningful that result actually is. Effect size fills that gap. The Publication Manual of the American Psychological Association (7th edition, Section 6.5) states that for each primary outcome, an effect size and confidence interval should be reported — and most major journals across the social, behavioral, and biomedical sciences now hold to an equivalent standard, whether or not they use APA style directly.

The reason this is a manuscript-writing concern and not only a statistics-course concern: a Results section that reports only a p-value leaves a reviewer unable to judge whether a “significant” finding is substantively important. With a large enough sample, even a trivially small difference becomes statistically significant (p < .05); with a small or underpowered sample, a genuinely large, meaningful effect can fail to reach significance. Effect size is what lets a reader — and a subsequent meta-analysis — evaluate the finding on its own terms, independent of the sample size a particular study happened to use.

Common effect-size statistics and what each one measures

Cohen’s d — a standardized mean difference between two groups, expressed in units of pooled standard deviation. Used for comparing group means (e.g., treatment vs. control on a continuous outcome).
Pearson’s r — already a standardized measure of linear association between two continuous variables; when r is the statistic of interest, it functions as its own effect size and no separate conversion is needed. r² (or R² in regression) expresses the proportion of variance explained.
Odds ratio (OR) and relative risk (RR) — effect-size measures for categorical or binary outcomes, common in clinical and epidemiological research. Unlike d, “no effect” corresponds to OR/RR = 1, not 0, which changes how the confidence interval should be read.
Eta-squared (η²) and partial eta-squared — proportion-of-variance measures commonly reported alongside ANOVA results.

Which statistic is appropriate depends on the design and the outcome’s measurement scale — a manuscript should not report Cohen’s d for a binary outcome or an odds ratio for a continuous one.

Effect size vs. statistical significance

These two numbers answer different questions and neither substitutes for the other in a Results section:

Statistical significance (p-value) answers: is this result unlikely to have occurred by chance alone, given the sample?
Effect size answers: how large is the observed difference, relationship, or association?

A manuscript that reports only one of the two is incomplete by current reporting standards. This is closely related to, but distinct from, the broader distinction between descriptive and inferential statistics: effect size is itself an inferential-style estimate (typically reported with a confidence interval), but its purpose is to quantify magnitude rather than to test whether an effect exists at all.

Interpreting magnitude: benchmarks and their limits

Jacob Cohen proposed conventional benchmarks for interpreting standardized effect sizes — commonly cited as small (d ≈ 0.2, r ≈ 0.1), medium (d ≈ 0.5, r ≈ 0.3), and large (d ≈ 0.8, r ≈ 0.5). These benchmarks are widely taught, but Cohen himself, and most current methodological guidance, caution against applying them mechanically: what counts as a meaningful effect size is field- and context-dependent. A small effect size in a large-scale public-health intervention can be practically important at population scale, while a “large” effect size in an underpowered pilot study may not replicate. Manuscripts should interpret effect-size magnitude against the relevant literature and practical stakes of the outcome, not against the generic benchmark alone.

Reporting effect size correctly in a Results section

Standard APA-style reporting places the effect size directly alongside the test statistic and p-value, for example: t(98) = 2.85, p = .005, d = 0.57. Best practice, reflected in APA guidance and in reporting checklists such as CONSORT for randomized trials, is to report the effect size together with its confidence interval, not as a bare point estimate — the interval communicates the precision of the estimate, which the effect size alone does not. This connects directly to a study’s experimental design: the design determines which effect-size statistic is appropriate and how precisely it can be estimated, since underpowered designs produce wide, uninformative confidence intervals around the effect size even when the point estimate looks large.

Frequently asked questions

Is effect size the same as statistical significance?

No. Statistical significance (the p-value) indicates whether an observed result is unlikely to be due to chance; effect size indicates how large that result is. A result can be statistically significant with a small effect size (common in large samples), or fail to reach significance despite a large effect size (common in small or underpowered samples).

Which effect size should I report?

It depends on the design and outcome type: Cohen’s d (or a related standardized mean difference such as Hedges’ g) for comparing two group means, Pearson’s r or R² for associations and regression, and odds ratio or relative risk for binary/categorical outcomes. Field-specific reporting guidelines (e.g., CONSORT, APA style) often specify or recommend a particular statistic for a given design.

Do all journals require effect size reporting?

Requirements vary by journal and field, but reporting an effect size alongside significance testing is now standard expectation across most major journals in psychology, education, medicine, and the social sciences, reflecting APA Publication Manual guidance and parallel recommendations from bodies such as the American Statistical Association.

Use in your systems

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