In the traditional hypothesis-testing framework, each gene is tested individually and then a stepwise adjustment procedure is applied both to control the family-wise type-1 error rate (FWER) and to declare individual genes associated [29]. This approach, related to the Bonferroni correction, achieves strong control of the FWER, which is the probability of at least one false positive being within the desired rate when there are any number of true positives. This is generally considered to be too conservative for genome-wide studies, however, because we can tolerate a small number of false positives if most true positives are detected. More preferable is weak control of FWER, which ensures that the probability of at least one false positive is within the desired rate only when there are no true positives. This is desirable, because we must defend against the possibility of there being no true associations in the sample, but it allows us to tolerate some false positives if some true positives are present.
