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).

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    $\begingroup$ You have access to R :) $\endgroup$ Mar 11, 2014 at 5:04

1 Answer 1


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.

  • $\begingroup$ It looks like the R program uses a different weighting scheme for the studies than what we used. We used the Hunter & Schmidt (2004) approach with sample-size weights, but it appears that the R program uses the inverse of estimated error variance which will result in a slightly different weighted average. Because we are basing our SAMD values on this different average (from R, vs. our computations), the results from R might not correspond precisely to our other analyses. Does anyone have thoughts about the similarity of these results and/or changing the R program to use sample size weights? $\endgroup$
    – jnk7711
    Mar 18, 2014 at 13:56
  • $\begingroup$ Yes, the default is to use 'inverse-variance' weights. You can get something closer to the H&S approach by using: rma(measure="COR", ri=ri, ni=ni, vtype="HO", method="HS", data=dat) (assuming the data frame is called dat and it contains variables ri and ni for the correlations and sample sizes). It's not exactly the same as the "H&S approach", but it should be closer. $\endgroup$
    – Wolfgang
    Mar 18, 2014 at 16:50

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