Simultaneous tests for finite families of hypotheses

Abstract

A procedure is proposed whereby R test statistics F=(F₁F₂…F_r)together with "randomly generated critical points" (C₁C₂…C_r) may be used to construct a simultaneous test for

a family containing R hypotheses. This procedure provides simultaneous tests having an exact prescribed type I error rate; the procedure does not require the distribution of F to be known. The simultaneous test is illustrated for making all pairwise comparisons in a one-way ANOVA model.

Keywords:

• Barnard’s test
• Birnbaum’s test
• simultaneous confidence intervals
• randomized test
• one-way ANOVA
• pairwise comparisons