Gravity in meta-analysis

Gravity is a measure of the weight that ought to be accorded to a particular study when applying meta-analysis to synthesize the results of several separate studies. Each of these individual studies would have been undetaken in broadly the same context and in order to study the same hypothesis. Meta-analysis is a statistical procedure that combines the results of the studies to produce an overall estimate of the effect size which should bre much improved over any individual estimate. However, in meta-analyses, there is often debate centered around the inclusion or exclusion of some number of studies, which critics would like to see included or excluded. In a simple meta-analysis, results of studies are averaged (albeit using weights according to their sample size and/or their internal variability) and, in this context, Geeproposed that jackknife methods could be used to examine study influence and detect outliers. The numerical measures associated with this way of assessing how similar one study is to the others was called the "gravity".
Examples of meta-analysis arise in the social sciences and also in medical studies. Effect sizes are usually expressed as an odds ratio or a standardized difference between the means of two groups.
Methodology
The idea behind the gravity concept is a type of jackknife approach, in which a form of meta-analysis is repeated several times, each time leaving out one of the studies. If there are k studies, k "leave-one-oue" results are obtained. The difference between the average of these k results and that when a particular study is omitted is taken as an index of "raw gravity." This difference, divided by the standard deviation of the k differences, may be taken as a Z-score, or "standardized gravity" that can be used to establish which studies might be unusually influential.
Gee<ref name="Gee" /> also observed that a similar idea can be applied using the more general case of "leave-n-out" jackknifing.

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