Global and multiple test procedures using ordered p-values - a review

This paper reviews global and multiple tests for the combination of n hypotheses using the ordered p-values of the n individual tests. In 1987, Rohmel and Streitberg presented a general method to construct global level a tests based on ordered p-values when there exists no prior knowledge regarding the joint distribution of the corresponding test statistics. In the case of independent test statistics, construction of global tests is available by means of recursive formulae presented by Bicher (1989), Kornatz (1994) and Firmer and Roters (1994). Multiple test procedures can be developed by applying the closed test principle using these global tests as building blocks. Liu (1996) proposed representing closed tests by means of "critical matrices" which contain the critical values of the global tests. Within the framework of these theoretical concepts, well-known global tests and multiple test procedures are classified and the relationships between the different tests are characterised.