Name: Bretz

Firstname: Frank

Title: Dr.

Institution: University of Hannover

Street: Herrenhaeuser Str. 2

City: Hannover

Zip-Code: 30419

Country: Germany

Phone: ++49-511-7625564

Fax: ++49-511-7624966


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.