$$\hat{\tau} = \frac{\sum_{i = 1}^K \frac{1}{\sigma_i^2} \hat{\tau_i}}{\sum_{i = 1}^K \frac{1}{\sigma_i^2}} $$

PartA Consider the case of K independent studies. Let 1%; denote each study 1's estimator of the effect and 01; the known standard error of that estimator (assume that we know the true SE). One approach to a metaanalysis assumes that each 722. is an unbiased estimator of a common effect parameter 1" and that differences between studies are attributable to sampling error. Consider the proposed combined estimator 'f' 22:1 317'? K 21:1 31? Find the expectation of %. Is it an unbiased estimator of T? 1