[R-meta] combining different effect sizes

[James Pustejovsky]

Hi Arne,

I assume you are talking about converting from metrics for binary outcomes
(odds ratios or risk ratios) into metrics for continuous outcomes. There
are methods for doing such conversions---one that comes up routinely is
converting from odds ratios into standardized mean differences. There are
several different formulas for doing so. Here are some relevant references:

Chinn, S. (2000). A simple method for converting an odds ratio to effect
size for use in meta‐analysis. Statistics in Medicine, 19(22), 3127-3131.
doi:10.1002/1097-0258(20001130)19:22<3127::AID-SIM784>3.3.CO;2-D
Borenstein, M., Hedges, L. V., Higgins, J. P. T. and Rothstein, H. R.
(2009) Converting Among Effect Sizes, in Introduction to Meta-Analysis (pp.
45-49). Chichester, England: John Wiley & Sons, Ltd.
doi:10.1002/9780470743386.ch7
Fleiss, J.L. & Berlin, J.A. (2009). Effect sizes for dichotomous data. In
Cooper, H., Hedges, L.V., & Valentine, Jeffrey C. (Eds.), The Handbook of
Research Synthesis and Meta-Analysis (2nd Ed) (pp. 237-254). New York, NY:
Russell Sage Foundation.
Haddock, C. K., Rindskopf, D., & Shadish, W. R. (1998). Using odds ratios
as effect sizes for meta-analysis of dichotomous data: A primer on methods
and issues. Psychological Methods, 3, 339–353.
Holling, H., Böhning, D., & Böhning, W. (2007). Meta-analysis of binary
data based upon dichotomized criteria. Zeitschrift für Psychologie/Journal
of Psychology, 215(2), 122-131. doi:10.1027/0044-3409.215.2.122
Sánchez-Meca, J., Marín-Martínez, F., & Chacón-Moscoso, S. (2003).
Effect-size indices for dichotomized outcomes in meta-analysis.
Psychological methods, 8(4), 448. doi:10.1037/1082-989x.8.4.448

Whether using such conversions makes sense depends on whether the modeling
assumptions behind them are reasonable in application. The motivating model
behind the conversions is that the binary outcome arises from dichotomizing
an underlying continuous variable. Under some distributional assumptions,
you can use the information in the binary variable to estimate the
standardized mean difference on the latent continuous variable. This tends
to be more reasonable when the binary variable really is a dichotomization
of a continuous variable that the other studies report. For example, if
most studies report academic performance on standardized tests, but one or
two studies report rates of proficiency (i.e., scoring above a benchmark
level) on similar tests, then it seems reasonable to try and recover the
SMD on the test. If you can't identify any coherent latent construct that
is dichotomized into the binary variable, then trying to convert seems less
reasonable.

If you do end up using a conversion, it seems nonetheless useful and
prudent to consider whether the type of outcome (binary vs. continous)
moderates the magnitude of effects.

James


On Tue, Feb 10, 2026 at 7:19 AM Arne Janssen via R-sig-meta-analysis <
r-sig-meta-analysis using r-project.org> wrote:

> L.S.,
>
> I have a very simple (perhaps even silly) question: I am interested in
> doing a meta-analysis using datasets that report means, standard deviations
> and sample sizes, whereas others report 2x2 tables or proportions  and
> sample sizes. After having calculated effect sizes with the appropriate
> escalc measure (SMD, RR, etc. respectively), does it make sense at all to
> combine all these effect sizes into one analysis with rma? My gut feeling
> is not, but I would like to be sure.
>
> Thanks very much in advance,
> Arne Janssen
> University of Amsterdam
> The Netherlands
>
>         [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-meta-analysis mailing list @ R-sig-meta-analysis using r-project.org
> To manage your subscription to this mailing list, go to:
> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>

	[[alternative HTML version deleted]]