Gudrun Bernhard (Novartis Pharma AG, Switzerland),

Markus Klein, Gerhard Hommel (University of Mainz, Germany)

Global and multiple test procedures using ordered p-values

We looked at global and multiple tests for the combination of n hypotheses that are based only on the ordered p-values of the individual tests for each of the n hypotheses.Two different situations were considered:

- Arbitrary dependencies among the test statistics; for this situation, Röhmel and Streitberg (1987) provided a general class of global tests.

- Independent test statistics; for this situation, a general class of global tests was described by Kornatz (1994) using recursive formulas.

Multiple test procedures that are based on global tests can be developed using the concept of critical matrices for closed tests (Wei Liu, 1996).

References:

  1. Klein,M. (1998). Multiple Testprozeduren: Step-down und Step-up. Diploma thesis, Mainz.

  2. Kornatz,C. (1994). Allgemeine Schrankentests und ihre Anwendung bei aufeinanderfolgenden Studien. Diploma thesis, Mainz.

  3. Liu, Wei (1996). Multiple tests of a non-hierarchical finite family of hypotheses. JRSS B 58, 455-461.

  4. Röhmel,J., Streitberg,B. (1987). Zur Konstruktion globaler Tests. EDV in Med. und Biol. 18, 7-11.