If family–wise error is too conservative, then do we need a genomewide significance threshold? We have argued that for the global null that no locus is associated, strong control of FWER is an acceptable proxy for weak control, FDR or Bayes factor approaches. Thus, if no locus is genomewide significant, we may conclude that no associations have been found, whereas if some loci are genomewide significant, other approaches can be used to decide which should be declared associated. It may be argued that the global null is not of interest, as the entire study is predicated on it being false. However, we feel that a significant global test is evidence that there is sufficient signal in the data to distinguish true from false positives. Given the uncertainty over what thresholds should be applied, the common pragmatic approach is to follow up associations in rank order, and this can be justified by a significant global test. Estimation of a genomewide significance threshold gives a baseline that can justify both pragmatic and principled approaches to selecting loci for follow–up.
