Step-up and step-down methods for testing multiple hypotheses in sequential experiments

Sequential methods are developed for testing multiple hypotheses, resulting in a statistical decision for each individual test and controlling the familywise error rate and the familywise power in the strong sense. Extending the ideas of step-up and step-down methods for multiple comparisons to sequential designs, the new techniques improve over the Bonferroni and closed testing methods proposed earlier by a substantial reduction of the expected sample size.