  We outline a Bayesian model-averaged meta-analysis for standardized mean
differences in order to quantify evidence for both treatment effectiveness
$\delta$ and across-study heterogeneity $\tau$. We construct four competing
models by orthogonally combining two present-absent assumptions, one for the
treatment effect and one for across-study heterogeneity. To inform the choice
of prior distributions for the model parameters, we used 50% of the Cochrane
Database of Systematic Reviews to specify rival prior distributions for
$\delta$ and $\tau$. The relative predictive performance of the competing
models and rival prior distributions was assessed using the remaining 50\% of
the Cochrane Database. On average, $\mathcal{H}_1^r$ -- the model that assumes
the presence of a treatment effect as well as across-study heterogeneity --
outpredicted the other models, but not by a large margin. Within
$\mathcal{H}_1^r$, predictive adequacy was relatively constant across the rival
prior distributions. We propose specific empirical prior distributions, both
for the field in general and for each of 46 specific medical subdisciplines. An
example from oral health demonstrates how the proposed prior distributions can
be used to conduct a Bayesian model-averaged meta-analysis in the open-source
software R and JASP. The preregistered analysis plan is available at
https://osf.io/zs3df/.
