Multiple hypothesis testing is a fundamental problem in statistical inference, and the failure to manage multiple testing problems has been highlighted as one of the elements contributing to the replicability crisis in science (Ioannidis 2015). Methodologies have been developed to manage the multiple testing situation by adjusting the significance levels for a family of hypotheses, in order to control error metrics such as the familywise error rate (FWER) or the false discovery rate (FDR).
Frequently, modern data analysis problems have a further complexity in that the hypotheses arrive sequentially in a stream.
This introduces the challenge that at each step, the investigator must decide whether to reject the current null hypothesis without having access to the future p-values or the total number of hypotheses to be tested, but with the knowledge of the historic decisions to date.
onlineFDR package provides a family of algorithms you can apply to a historic or growing dataset to control the FDR or FWER in an online manner. At a high-level, these algorithms rely on a concept called “alpha wealth” in which experiments cost some amount of error from your “budget” but a discovery earns some of the budget back.