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In meta-analysis the random-effects model is often used to account for heterogeneity. The model assumes that heterogeneity has an additive effect on the variance of effect sizes. An alternative model which assumes multiplicative heterogeneity has been little used in the medical-statistics community, but is widely used by particle physicists. In this paper we compare the two models using a random sample of 448 meta-analyses drawn from the Cochrane Database of Systematic Reviews. In general, differences in goodness of fit are modest. The multiplicative model tends to give results that are closer to the null, with a narrower confidence interval. Both approaches make different assumptions about the outcome of the meta-analysis. In our opinion, the selection of the more appropriate model will often be guided by whether the multiplicative model's assumption of a single effect size is plausible.