Multiple Tests for Different Sets of Variables Using a Data‐Driven Ordering of Hypotheses, with an Application to Gene Expression Data

A multiple parametric test procedure is proposed, which considers tests of means of several variables. The single variables or subsets of variables are ordered according to a data-dependent criterion and tested in this succession without alpha-adjustment until the first non-significant test. The test procedure needs the assumption of a multivariate normal distribution and utilizes the theory of spherical distributions. The basic version is particularly suited for variables with approximately equal variances. As a typical example, the procedure is applied to gene expression data from a commercial array.