Power comparisons of some step-up multiple test procedures

Powers of some recently proposed step-up multiple test procedures are compared. These include procedures of Hommel (1988), Hochberg (1988) and Rom (1990), which are based on the individual p-values of the test statistics. The powers of the normal theory based step-up procedure of Dunnett and Tamhane (1992) are also included to assess further gains due to taking the correlations among the test statistics into account. Both the Hommel and Rom procedures are uniform improvements over the Hochberg procedure, but are more complicated to use (particularly the former). Power calculations show that they both offer only marginal improvements.