I need to compute the sample-adjusted meta-analytic deviancy (SAMD) as part of an outlier search with meta-analytic data. Because we have a very large amount of meta-analytic data, computing this statistic by hand would take a little longer than forever. Does anyone know of an SPSS, Excel, or MPLUS syntax/macro available to compute SAMD? I do not have access to other statistical packages (e.g., SAS).
For those who do not know what the "sample-adjusted meta-analytic deviancy (SAMD)" statistic is -- it's just externally studentized residuals (see Wikipedia) for meta-analytic data (also called 'studentized deleted residuals'). See:
Huffcutt, A. I., & Arthur, W., Jr. (1995). Development of a new outlier statistic for meta-analytic data. Journal of Applied Psychology, 80, 327-334.
The authors actually describe SAMD as a sort of DFFITS value (see Wikipedia), but that characterization isn't quite accurate. And their formulas only apply to the very simplest meta-analytic model (without moderators or residual heterogeneity).
If you want a more thorough presentation on outlier and influence diagnostics for meta-analytic data, I would suggest:
Viechtbauer, W., & Cheung, M. W.-L. (2010). Outlier and influence diagnostics for meta-analysis. Research Synthesis Methods, 1(2), 112-125.
Externally studentized residuals are also described (but more generally, also for random-effects models and also in the context of mixed-effects meta-regression, with the case covered by Huffcutt & Arthur just as a special case). The logical extension of DFFITS to meta-analytic data is also described (and so are Cook's distances, DFBETAS, COVRATIO, and a few others).
All of the outlier and influence diagnostics described in that paper are implemented in the
metafor package for R (package website). An example illustrating how one can obtain these statistics with the package can be found here.
And as a final note: The idea of computing externally studentized residuals for meta-analytic data was already described by Hedges and Olkin in 1985:
Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. London: Academic Press.
See chapter 12. They also cover meta-regression models, but not random/mixed-effects models.