Table 1.

Estimated unknown variance components for 3 previously used examples, using 3 different estimation methods

Dataset	PM		DL		REML
	${\widehat{\tau }}_{\beta }^2$	${\widehat{\tau }}_{\omega }^2$	${\widehat{\tau }}_{\beta }^2$	${\widehat{\tau }}_{\omega }^2$	${\widehat{\tau }}_{\beta }^2$	${\widehat{\tau }}_{\omega }^2$	95% CI: ${\tau }_{\beta }^2$	95% CI: ${\tau }_{\omega }^2$
PC	0	0	0	0	0	0	(0, 0.07)	(0, 0.62)
CDE	0.36	0.52	0.25	0.30	0.10	0.54	(0, 1.67)	(0, 3.96)
OAK	0.35	0	0.18	0	0.18	0	(0.09, 0.31)	(0, 0.12)

Point estimates of ${\tau }_{\beta }^2$ and ${\tau }_{\omega }^2$ are given for all 3 methods. Approximate 95% confidence intervals (CIs) using REML are also given and are obtained from the profile likelihood.

Abbreviations: PM, the proposed Paule and Mandel estimation method; DL, a generalisation of DerSimonian and Laird's univariate method; REML, restricted maximum likelihood.