Online control of the familywise error rate

Biological research often involves testing a growing number of null hypotheses as new data are accumulated over time. We study the problem online control familywise error rate, that is an priori unbounded sequence ( p-values) one by time without knowing future, such with high probability there no false discoveries in entire sequence. This paper unifies algorithmic concepts developed for offline (single batch) rate and discovery to develop novel methods. Though many methods (e.g., Bonferroni, fallback procedures Sidak’s method) can trivially be extended setting, our main contribution design new, powerful, adaptive algorithms when p-values independent or locally dependent Our numerical experiments demonstrate substantial gains power, also formally proved idealized Gaussian model. A promising application International Mouse Phenotyping Consortium described.