Effect size

Researchers want to know not just whether an intervention has an effect but how big that effect is [1]. Effect sizes fall into two families: the d family, made up of standardized mean differences, and the r family, which measures strength of association [1]. A d-family effect size is the difference between observations divided by their standard deviation, which puts studies that used different scales on a common footing [1]. Hedges' g is a corrected version of Cohen's d [1].

For yes-or-no outcomes, the CONSORT reporting guideline recommends giving both absolute and relative effect sizes [2]. It also asks trials to report, for each primary and secondary outcome, the estimated effect size with its precision, such as a 95% confidence interval [2]. A Cochrane review comparing placebo with no treatment in clinical populations, for instance, reported an overall standardized mean difference of -0.23 (95% CI -0.28 to -0.17), where a negative value favored placebo [3].

Standardized effect sizes let researchers convey practical significance, meaning what a finding implies for daily life, instead of only statistical significance [1]. They also allow conclusions across studies, which is what a meta-analysis does [1].

Cohen's labels of small (d = 0.2), medium (d = 0.5) and large (d = 0.8) are widely quoted, but Lakens notes they are arbitrary and should not be interpreted rigidly [1]. Effect size estimates also have their own confidence intervals [1], so a single number on its own can look more certain than it is.

Our research summaries aim to give effect sizes as each paper reports them and to name the comparison, so a reader can see both the size of a result and what it was measured against.

• Confidence interval: the range of uncertainty around an effect size.
• Meta-analysis: pooling effect sizes across studies.
• Placebo: a common comparison in trials.