Effect size

Effect size is a family of statistics that express how large a measured difference or relationship is, independent of how many people were studied. A p-value addresses whether a result is likely to reflect a real phenomenon; an effect size addresses how large that phenomenon appears to be — and a study can produce very different answers to each question.

Several measures fall under the term. Cohen's d expresses the difference between two group means in standard-deviation units. An odds ratio or relative risk expresses how much more likely an outcome is in one group than another. Correlation coefficients such as Pearson's r express the strength of a linear relationship. Which measure is appropriate depends on the study design and the outcome being measured.

What this design can establish

A well-reported effect size tells you the magnitude of a difference in standardised terms — terms that can be compared across studies that measured the same outcome on different scales or in different populations. That comparability is what makes effect sizes the building block of meta-analysis: when dozens of trials have measured similar outcomes in different ways, a shared metric lets a synthesis estimate the overall magnitude across all of them.

Effect size also provides a check on whether a statistically significant result is practically meaningful. A difference can clear a significance threshold in a large enough sample while remaining too small to matter in any practical sense. Reporting the effect size alongside the p-value lets a reader make that judgment independently of the statistical conclusion.

What it cannot

Effect size says nothing about whether a finding is real. A large Cohen's d in a poorly controlled trial with a confounded design is evidence of very little — it reports the size of the measured difference, not whether the measurement was valid or the comparison was fair.

It also cannot say whether an effect will be noticeable to a given person. Effect sizes are population-level summaries: they describe averages across groups, not the spread of responses within them. An effect that is large in aggregate may be imperceptible to many individuals and substantial for a few.

The inference a reader is most likely to make — and the one to hold carefully — is that a larger effect size signals a more trustworthy finding. It does not. Effect size reports magnitude; it carries no information about whether confounders were controlled, whether the study design supports the claim, or whether the result will replicate.