Michael Weichert (Cap Gemeni, Germany)

Determining all logical dependencies among pairwise hypotheses using graphs

In a one-way layout one often is interested in the pairwise copmarison of some or all the treatments. When conducting more than one test on the data one is confronted with the problem of substaining the multiple level of the experiment. One way of controlling the multiple level is to use the closure testing principle. When constructing the closure testing system one has to determine the logical dependecies among the hypotheses. The logical dependecies are of two kinds. First the intersection of some hypotheses may include some other ones. (e.g. ) Second an intersection hypothesis could be empty, so it is not part of the closure test system. (e.g. ) The problem of dertermining these dependencies is solved by mapping the relevant intersection hypotheses onto a graph. When only twosided hypotheses are of interest, an undirected graph is used, otherwise a directed graph is used. The results can be extended to handle systems of hypotheses including shifted hypotheses and equivalence hypotheses.

References:

- Berhard, G. (1991), Computergestützte Durchführung von multiplen Testprozeduren - Verbesserte Algorithmen und Powervergleich-, Dissertation, Universität Mainz
- Hommel, G. (1999), Concepts for the description of logical relationships among hyotheses, Vortrag auf der AG Sitzung "Multiple Verfahren", Mainz
- Marcus, R., Perlitz, E., Gabriel, K.R. (1976), On closed testing procedures with special reference to ordered analysis of variance, Biometrica 63
- Weichert, M. (2000), Robuste Mittelwertvergleiche mit gartenbaulichen Anwendungen, Dissertation, Universität Hannover