extent of the uncertainty. Commonly, random effects are estimated with a 95% CI that captures the uncertainty about the mean effect, but ideally one should also examine the uncertainty of the distribution of effects across populations. This is provided by the prediction interval. An approximate (1−α)% prediction interval for the effect in an unspecified study can be obtained from the estimate of the mean effect μ̂, its estimated standard error, and the estimate of the between-study variance τ̂2 by
