ABSTRACT
In this chapter, we give a survey of multiple test procedures (MTPs) based on p-values. These MTPs are widely used in practice since they are easy to apply and do not make any strong distributional or joint dependence assumptions. First, we review stepwise MTPs that can be derived as shortcuts to the closure procedure of Marcus, Peritz and Gabriel (1976) using the Bonferroni or the Simes (1986) tests for testing local intersection hypotheses. They include the well-known MTPs of Holm (1979), Hochberg (1988), Hommel (1988), fixed sequence (Maurer, Hothorn and Lehmacher 1995) and fallback (Wiens 2003, Wiens and Dmitrienko 2005). Next, we review gatekeeping procedures for hierarchically ordered families of hypotheses with logical relations among them (Dmitrienko and Tamhane 2007). This is followed by a brief review of the graphical approach to constructing and visualizing sequentially rejective Bonferroni MTPs (Bretz et al. 2009, Bretz et al. 2011). Finally, we review group sequential versions of the Holm and Hochberg MTPs (Maurer and Bretz 2013). Simple numerical examples are used to illustrate various procedures.
