Table 3.

Properties of estimates for μ and τ ² from the simulation study with K = 5 studies, using 1000 simulations for each τ ² value. In each case, IS denotes values using Bayesian methods by importance sampling. ‘Z length’ denotes the average length of the nominal 95% interval for μ using the standard normal quantile, and ‘Z coverage’ denotes the proportion of nominal 95% intervals that cover the true value, using the standard normal quantile.

Properties of estimates for μ
	Empirical mean		Empirical std dev		Z length		Z coverage
	IS	MCMC	IS	MCMC	IS	MCMC	IS	MCMC
τ 2 = 0	− 0.001	− 0.001	0.106	0.106	0.771	0.771	0.9993	1
τ 2 = 0.029	0.003	0.003	0.143	0.144	0.800	0.805	0.995	0.995
τ 2 = 0.069	0.001	0.001	0.170	0.169	0.840	0.842	0.985	0.985
τ 2 = 0.206	0.005	0.005	0.260	0.260	0.971	0.984	0.996	0.996
τ 2 = 1.302	0.013	0.012	0.556	0.554	1.654	1.839	0.991	0.992
Properties of estimates for τ2
	Empirical mean		Empirical std dev
	IS	MCMC	IS	MCMC
τ 2 = 0	0.064	0.064	0.018	0.018
τ 2 = 0.029	0.073	0.073	0.027	0.027
τ 2 = 0.069	0.084	0.084	0.040	0.040
τ 2 = 0.206	0.141	0.142	0.112	0.111
τ 2 = 1.302	0.767	0.787	0.646	0.682

MCMC, Markov chain Monte Carlo.