Optimally weighted, fixed sequence and gatekeeper multiple testing procedures

By Peter Westfall, A. Krishen. 2001

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LOPSIDED REASONING ON LOPSIDED TESTS AND MULTIPLE COMPARISONS (2012, background): “In going from αS = 0.05 to q = 0.05, one is simply relaxing the criteria for ‘statistical significance’, not gaining power in any substantive, cost-free way.”
On the Simes inequality and its generalization (2008, methodology): “Besides theoretically validating the Type I error rate control of the Simes (1986) test, which has now been frequently used in place of the Bonferroni test in many scientific investigations (Dmitrienko et al. [7], Hommel et al. [11], Meng et al. [16], Neuhauser et al. [17], Rosenberg et al. [19], So”
The Sequential Rejection Principle of Familywise Error Control (2010, background): “We illustrate this for the basic unweighted serial [Westfall and Krishen (2001)] and parallel [Dmitrienko, Offen and Westfall (2003)] gatekeeping strategies for two families, G1 and G2.”