Figure 1. Organizational flowchart of a meta-analysis. Different studies (S1–S3) report means and standard deviations of a given response variable for a treatment and a corresponding control. From each study, the treatment effect size is calculated from the difference or ratio of the averages (red), whereas the variance within each study is pooled to allow the estimation of sampling variances for each study (blue). The general tendency of the experiments can then be synthesized by using unweighted or weighted meta-analyses. The significance of the effect across studies can be tested by calculating 95% confidence intervals around the average effect size.

Figure 2. Illustration of effect sizes along sample data sets. A data set was constructed assuming a treatment and a control, where the average for the response variable was set as 1 for the control and varies between 0.001 and 100 in the treatment. It was assumed that the standard deviation was either 10% or 100% of the mean. The diagrams show the corresponding effect size measured as Hedges' d (blue and green) or ln R (red) across the range of treatment values in either linear (a) or log-transformed (b) parameter space. (c) The effect size±sampling variance for this data set.

Figure 3. Illustration of a funnel plot. The graphic representation of effect sizes over sample sizes allows identifying a potential publication bias, if (as indicated by an arrow) there is a systematic lack of small effect sizes around zero.