What do results from coordinate-based meta-analyses tell us?

Coordinate-based meta-analyses (CBMA) methods, such as Activation Likelihood Estimation (ALE) and Seed-based d Mapping (SDM), have become an invaluable tool for summarizing the findings of voxel-based neuroimaging studies. However, the progressive sophistication of these methods may have concealed two particularities of their statistical tests. Common univariate voxelwise tests (such as the t/z-tests used in SPM and FSL) detect voxels that activate, or voxels that show differences between groups. Conversely, the tests conducted in CBMA test for "spatial convergence" of findings, i.e., they detect regions where studies report "more peaks than in most regions", regions that activate "more than most regions do", or regions that show "larger differences between groups than most regions do". The first particularity is that these tests rely on two spatial assumptions (voxels are independent and have the same probability to have a "false" peak), whose violation may make their results either conservative or liberal, though fortunately current versions of ALE, SDM and some other methods consider these assumptions. The second particularity is that the use of these tests involves an important paradox: the statistical power to detect a given effect is higher if there are no other effects in the brain, whereas lower in presence of multiple effects.