effectsize

Effect size is a quantitative measure of the magnitude of a phenomenon. It characterizes how large an observed effect is, independent of sample size, and is used to gauge practical or clinical significance rather than solely statistical significance. Effect sizes facilitate comparisons across studies and are central to meta-analysis and power calculations.

Common measures of effect size include Cohen's d, which standardizes the difference between two group means by a pooled standard deviation; Pearson's r, the correlation coefficient that expresses the strength of a linear relationship; odds ratio and relative risk for binary outcomes; and analysis of variance measures such as eta squared and partial eta squared. Cohen's f is another standardized measure used in ANOVA contexts. Bias corrections exist, such as Hedges' g, which adjusts Cohen's d for small-sample bias.

Interpretation of effect sizes depends on context. General benchmarks for Cohen's d are often cited as small around 0.2, medium around 0.5, and large around 0.8, while benchmarks for r are roughly 0.1, 0.3, and 0.5. However, the practical significance of an effect is context-specific and should consider measurement scales, domain expectations, and study design. Confidence intervals around effect sizes reflect precision and sample variability, and larger samples yield tighter intervals.

Effect sizes are widely used in reporting research, comparing results across studies, informing sample size planning, and guiding decisions about practical importance beyond p-values. Limitations include dependence on measurement reliability and study design, which can influence the magnitude and interpretability of effect sizes.