Computing effect sizes

With the data extracted in Coding primary studies, it is necessary to compute, for each study, an effect size, its variance, standard error, and confidence interval. The effect size is a measure of the magnitude of a relationship between two variables or a difference between groups. Main types of effect sizes are based on:

• means (Cohen's d, Hedges' g, raw unstandardized difference)
• binary data (risk ratio, odds ratio, risk difference)
• correlations (Pearson's correlations, Fisher's Z)
• survival data (hazard ratio)

The variance, standard error, and confidence interval provide an estimate of the precision of an effect size. The best way of reporting these results is through a forest plot — a plot of effect sizes (with confidence intervals) of all the studies included in the meta-analysis. See Methods and formulas for the exact effect-size formulas.

Effect sizes are computed exactly when a study reports the raw ingredients (e.g., means, standard deviations, and sample sizes for Cohen's d); when it doesn't, they can sometimes be approximated from a reported significance test instead, but that's a fallback, not a first choice — the resulting estimate is less precise. Rules of thumb exist for interpreting magnitude (d around 0.2/0.5/0.8, or r around .1/.25/.45, as small/medium/large) but they're a starting point at best: the same absolute effect can be trivial in one research area and remarkable in another, so it's the study topic and methodology that should ultimately drive the interpretation, not the cutoff.

The result of this step is an effect size, variance, and confidence interval for every study, ready to be combined into an overall estimate in Aggregating effect sizes.