Fig. 1

Implementation of the methods SOMA, MAMA, COMA, and REMA (see Table 1) to simulated data. For a given scenario (characterized by a true mean effect size \(\mu\), a number of datasets (K), a number of data per dataset (N), a level of redundancy (P), and a level of precision), a hierarchical Gaussian model is used to generate K datasets, each including N data (effect sizes and standard errors). A 1st order MA is performed using each dataset in turn, generating K mean effect sizes (\({\Delta }_{1},{\Delta }_{2},{\dots , \Delta }_{k}\dots ,{\Delta }_{K}\)) and standard errors \(({\sigma }_{1},{\sigma }_{2},{\dots , \sigma }_{k}\dots ,{\sigma }_{K}\)). These quantities are used to implement the methods SOMA, MAMA, and COMA (see text). In addition, the K datasets are merged to produce a single global dataset used to implement the method REMA