Effect Size

Definition

Effect size is a quantitative measure of the magnitude of a difference or relationship observed in the data, independent of sample size. Common effect-size statistics include Cohen's d (standardised mean difference), the odds ratio, Pearson's r, and R² (proportion of variance explained). Effect sizes are essential in power analysis and meta-analysis.

Why It Matters

Statistical significance can be achieved with trivial effect sizes simply by collecting a very large sample. Effect size tells you whether the finding matters in practice. Journals, funding bodies, and evidence-based practice guidelines increasingly require effect-size reporting alongside p-values to support meaningful interpretation and decision-making.

Example

Two studies both report a statistically significant improvement in reading scores after a tutoring programme. Study A (n = 50) finds Cohen's d = 0.8, a large effect that educators would consider meaningful. Study B (n = 10,000) finds Cohen's d = 0.05, a negligible effect that is statistically significant only because of the enormous sample. Effect size reveals that only Study A's result is practically important.

Related Terms

• Statistical Significance
• P-Value
• Statistical Power
• Sample Size
• Meta-Analysis (effect sizes are the currency of meta-analysis)

Software Notes

• SPSS: Cohen's d is not produced automatically by most procedures. Calculate manually from means and standard deviations, or use the Effect Size extension. For ANOVA, partial eta-squared is reported in the Tests of Between-Subjects Effects table.
• R: effsize::cohen.d(group1, group2) for Cohen's d. lmeta::r2() for R². psych::omega() for omega-squared in ANOVA.
• Stata: esize twosample y, by(group) for Cohen's d in Stata 13+. esizei for immediate entry of summary statistics. regress y x reports R² directly.