Gravity (social science methodology)
- Gravity (social science methodology)
Social science results are often subjected to meta analysis, which is a statistical procedure that combines the results of studies to produce an overall estimate of the effect size. The effect size is usually expressed as an odds ratio or a standardized difference between the means of two groups.
Debate is often centered around the inclusion or exclusion of some number of studies, which critics would like to see included or excluded. As studies are commonly weighted according to their sample size and/or their internal variability, Gee [http://www.cphjournal.com/archive_journals/V1_I1_Gee_52-75_7_05.pdf] proposed that jackknife methods [http://en.wikipedia.org/wiki/John_Tukey] [http://en.wikipedia.org/wiki/Resampling_%28statistics%29#Jackknife] could be used to examine study influence and detect outliers. By re-computing the meta-analysis once for each of "k" studies, where each study is individually excluded, "k" results are obtained. The difference between the average of these "k" results and each study's individual result (when 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.
In the seminal article on the topic, Gee [http://www.cphjournal.com/archive_journals/V1_I1_Gee_52-75_7_05.pdf] also observed that this type of jackknifed meta-analysis is a special case in combinatorics wherein "k" objects (studies) are combined "k-1" at a time, resulting in "k" estimates. The extension of this logic implies that it is possible to study the behaviour of meta-analytic indices through the more general approach of combinatorial meta analysis by computing results for "k" studies taken 1, 2, 3 ... "k-1, k" at a time.
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