Is precision-based weighting central to meta-analysis? Borenstein et al. (2009) write that for meta-analysis to be possible all that is necessary is that:
- Studies report a point estimate which can be expressed as a single number
- Variance can be computed for that point estimate
It's not immediately clear to me why (2) is true. But, indeed, all of the widely accepted methods of meta-analysis rely on precision-based (i.e. inverse variance) weighting schemes, which do require an estimate of variance for each study's effect size. Note that while Hedges' Method (Hedges & Olkin, 1985; Hedges & Vevea, 1998) and Hunter and Schmidt's Method (Hunter & Schmidt, 2004) both basically use sample size weighting, these methods apply only to normalized mean differences, and thus require a standard deviation elsewhere.
This strikes me as odd, since meta-analysis is typically defined much more broadly, as "a set of statistical methods for systematically combining the results of multiple studies," or something similar. Is there a more specific description for meta-analysis which explains why inverse-variance weighting is unavoidable? Or alternately, is it possible to conduct a systematic review without access to the variance for each effect size and still call the result a meta-analysis? Could one, for instance, use sample-size weighting in a study where effect size was defined as raw mean difference? How would that effect the consistency and efficiency of the resulting mean effect size?