Institution: University of Hannover
Street: Herrenhaeuser Str. 2
Authors: Frank Bretz (University of Hannover, Germany) Peter Westfall (Texas Tech University, USA)
Title: Power of Closed Test Procedures
Abstract: Analytic formulas are developed for various types of power and error rates of some closed testing procedures. The formulas involve non-convex regions that may be integrated with high, pre-specified accuracy using available software. The non-convex regions are represented as a union of hyper-rectangles. These regions are transformed to the unit hypercube, then summed, to create an expression for power that is a single multidimensional integral of a function defined on the unit hypercube. This function is then evaluated using existing quasi-Monte Carlo methods that are known for their accuracy. Applications include individual, average, complete, and minimal power, for closed pairwise comparisons (max T-based), as well as fixed sequence and non-pairwise comparisons.