KONSİLWhat is effect size?
Effect size is a number showing how big a group difference or an association between variables is. It is reported as a raw difference, in standard deviation units (Cohen’s d, Hedges' g), or as an odds ratio or correlation r, and answers the ‘how much?’ that a p-value cannot.
The absolute effect size is the raw difference between group means (for example 5 mmHg). According to Sullivan and Feinn (2012) it is useful when variables have intrinsic meaning, while standardized indices are useful when measurements have none or studies use different scales. According to Lakens (2013), for independent groups Cohen’s d is the mean difference divided by the pooled standard deviation, and Hedges' g is d corrected for small-sample bias. The Cochrane Handbook calls this measure the standardized mean difference (SMD) and uses Hedges' g.
Besides Cohen’s d, Sullivan and Feinn (2012) list the odds ratio for binary outcomes and the correlation coefficient r for linear relationships between continuous variables as effect size indices; the Cochrane Handbook (chapter 6) gives the risk ratio, odds ratio and risk difference for binary outcomes. Effect size is an input of power analysis. According to the 2016 ASA statement, a p-value does not measure the size of an effect or the importance of a result.
Cohen’s values of d = 0.2, 0.5 and 0.8 for small, medium and large effects are conventions. Lakens (2013) calls them arbitrary, advises against rigid use and recommends comparing the effect with other findings in the field. The Cochrane Handbook adds that some methodologists find such generic interpretation problematic because the importance of a finding to patients depends on context.
Example
In a hypothetical study the intervention group’s mean is 24, the control group’s is 20 and the pooled standard deviation is 8, so the raw difference is 4 points and Cohen’s d = (24 − 20) / 8 = 0.50. With 20 participants per group, Hedges' g = 0.50 × (1 − 3 / (4 × 40 − 9)) = 0.490.
A point to watch
According to Lakens (2013), Cohen’s benchmarks of d = 0.2 / 0.5 / 0.8 are arbitrary and should not be applied mechanically; relating an effect to other effects in the field and explaining its practical consequences is the better route. According to the Cochrane Handbook, some methodologists find such generic interpretation problematic because the importance of a finding to patients depends on context.
Related terms
Guides and tools
Sources
- Using Effect Size—or Why the P Value Is Not Enough — Journal of Graduate Medical Education, 2012
- Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs — Frontiers in Psychology, 2013
- Cochrane Handbook for Systematic Reviews of Interventions, Chapter 6: Choosing effect measures and computing estimates of effect — Cochrane, 2024
- Cochrane Handbook for Systematic Reviews of Interventions, Chapter 15: Interpreting results and drawing conclusions — Cochrane, 2024
- A power primer — Psychological Bulletin (American Psychological Association), 1992
- Statistical Power Analysis for the Behavioral Sciences (2nd ed.) — Lawrence Erlbaum Associates (Routledge), 1988
- The ASA’s Statement on p-Values: Context, Process, and Purpose — The American Statistician (American Statistical Association), 2016