Table 2.

Summary of the four meta-analysis examples

Meta	k	I 2	Equal- α	W-optimal	${\alpha }_2^{\ast }$	Width
Analysis			CI (τ)	interval (τ)		Ratio
CERVIX3	5	56 %	(0, 1.287)	(0, 1.048)	0.050	0.814
NSCLC4	11	75 %	(0.227, 0.887)	(0.193, 0.824)	0.040	0.954
NSCLC1	17	45 %	(0.013, 0.426)	(0.028, 0.436)	0.021	0.986
CERVIX1	18	62 %	(0.201, 0.707)	(0.182, 0.678)	0.035	0.982

I ² is the heterogeneity statistic of Higgins and Thompson [28]. In each case we show the equal tailed (α ₁=α ₂=0.025) 95 % confidence interval for τ, the W-optimal interval for τ, the value of ${\alpha }_2^{\ast }$ that provides the W-optimal interval (also for τ) and the ratio of the width of the W-optimal interval and the equal tailed confidence interval. In each case we see that there is reduction in the interval width by adopting α ₂>>α ₁