Different metrics have been proposed for testing the presence and measuring the amount of between-study heterogeneity. Cochran's Q statistic [19] is provided by Q = Σ wiF (di−dF +)2 where dF + is the summary effect size by fixed effects, di are the study-specific effect sizes and wiF is the weight of each study (based on Mantel-Haenszel methods). The statistic follows a x 2 distribution with k-1 degrees of freedom (k is the number of studies or datasets combined), and it is typically considered significant at the α = 0.10 level. The original Science publications used this test to document whether there is or not between-study heterogeneity. However, this test is grossly underpowered, when there are very few studies. Also with small studies, the confidence intervals of each one may be very large, so the same problem of lack of power may still persist. Of note, Q is used in the estimation of the between-study variance, given by . The ratio of τ over the effect size conveys the extent of variability (between-study standard deviation) as compared with the effect size.
