<annotation encoding="application/x-tex">\text{se} = 0.085</annotation></semantics></math>).
The larger standard error is a natural consequence of accounting for the
dependency between the effect sizes. Because the effect sizes are
dependent, they contribute less additional information than independent
effect sizes would. Specifying the hierarchical model then accounts for
the dependency by estimating similarity between the estimates from the
same cluster (school) and discounting the information borrowed fr