Comparative analysis of meta-analysis methods: when to use which?

Background: Several meta-analysis methods can be used to quantitatively combine the results of a group of experiments, including the weighted mean difference, statistical vote counting, the parametric response ratio and the non-parametric response ratio. The software engineering community has focused on the weighted mean difference method. However, other meta-analysis methods have distinct strengths, such as being able to be used when variances are not reported. There are as yet no guidelines to indicate which method is best for use in each case. Aim: Compile a set of rules that SE researchers can use to ascertain which aggregation method is best for use in the synthesis phase of a systematic review. Method: Monte Carlo simulation varying the number of experiments in the meta analyses, the number of subjects that they include, their variance and effect size. We empirically calculated the reliability and statistical power in each case Results: WMD is generally reliable if the variance is low, whereas its power depends on the effect size and number of subjects per meta-analysis; the reliability of RR is generally unaffected by changes in variance, but it does require more subjects than WMD to be powerful; NPRR is the most reliable method, but it is not very powerful; SVC behaves well when the effect size is moderate, but is less reliable with other effect sizes. Detailed tables of results are annexed. Conclusions: Before undertaking statistical aggregation in software engineering, it is worthwhile checking whether there is any appreciable difference in the reliability and power of the methods. If there is, software engineers should select the method that optimizes both parameters.