Consider the problem of testing multiple null hypotheses. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. However, if s is large, control of the FWER is so stringent that the ability of a procedure which controls the FWER to detect false null hypothese...

Testing a sequence of pre-ordered hypotheses to decide which of these can be rejected or accepted while controlling the familywise error rate (FWER) is of importance in many scientific studies such as clinical trials. In this paper, we first introduce a generalized fixed sequence procedure whose critical values are defined by using a function of the numbers of rejections and acceptances, and wh...

There are various methods for obtaining the preference vector of pair-wise comparison matrix factors. These methods can be employed when the elements of pair-wise comparison matrix are crisp while they are inefficient for fuzzy elements of pair-wise comparison matrix. In this paper, a method is proposed by which the preference vector of pair-wise comparison matrix elements can be obtained even ...

2 Methods 5 2.1 Multiple hypothesis testing framework . . . . . . . . . . . . . 5 2.2 Test statistics null distribution . . . . . . . . . . . . . . . . . 11 2.3 Single-step procedures for control of general Type I error rates θ(FVn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Step-down procedures for control of the family-wise error rate 16 2.5 Augmentation multiple tes...

We consider a clinical trial with a primary and a secondary endpoint where the secondary endpoint is tested only if the primary endpoint is significant. The trial uses a group sequential procedure with two stages. The familywise error rate (FWER) of falsely concluding significance on either endpoint is to be controlled at a nominal level α. The type I error rate for the primary endpoint is cont...