Advances in p-Value Based Multiple Test Procedures

In this article we review recent advances in [Formula: see text]-value-based multiple test procedures (MTPs). We begin with a brief review of the basic tests of Bonferroni and Simes. Standard stepwise MTPs derived from them using the closure method of Marcus et al. (1976) are discussed next. They include the well-known MTPs of Holm (1979), Hochberg (1988) and Hommel (1988), and their extensions and improvements. This is followed by stepwise MTPs for a priori ordered hypotheses. Next we present gatekeeping MTPs (Dmitrienko and Tamhane, 2007) for hierarchically ordered families of hypotheses with logical relations among them. Finally, we give a brief review of the graphical approach (Bretz et al., 2009) to constructing and visualizing gatekeeping and other MTPs. Simple numerical examples are given to illustrate the various procedures.