Street: Langenbeckstrasse 1
Authors: Hommel, Gerhard; Bernhard, Gudrun
Title: Two- and one-sided tests for a set of linear contrast hypotheses
Abstract: We consider a set of hypotheses based on linear contrasts and multiple tests that control the familywise error rate. For two-sided testing problems, all intersections of hypotheses need to be determined in order to perform the closure test procedure. Two different concepts based on matrix algebra for determining the intersection hypotheses, have been described by Westfall (1997) and Hommel and Bernhard (1994). It is shown that both concepts lead to the same multiple test procedure. For one-sided testing problems, Westfall (1997) proposed to use the same set of intersection hypotheses, as for the two-sided case, but with one-sided p-values. However, this approach does not necessarily control directional errors. Therefore, we propose to use all intersections resulting from the set of one-sided null hypotheses. When considering only pairwise one-sided comparisons, graph-theoretic methods can be applied (Weichert, 1999). For more general contrasts, a method based on evaluating the entire hypotheses space is suggested.
References: Hommel, G., Bernhard, G. (1994). A rapid algorithm and a computer program for multiple test procedures using logical structures of hypotheses. Comp.Meth.Prog. in Biomedicine 43, 213-216.
Weichert, M.(1999). Robuste Mittelwertvergleiche mit gartenbaulichen Anwendungen. Ph.Thesis, Hannover/Germany.
Westfall, P.H. (1997). Multiple testing of general contrasts using logical constraints and correlations. J.Amer.Stat.Ass. 92, 299-306.