Statistica Sinica 16(2006), 227-234

ON ADAPTIVE TESTING IN ORTHOGONAL

SATURATED DESIGNS

Daniel T. Voss and Weizhen Wang

Wright State University

Abstract: Adaptive, size-$\alpha$ step-down tests are provided for the analysis of orthogonal saturated designs. The tests work effectively under effect sparsity, and include as special cases the individual nonadaptive tests of Berk and Picard (1991) and the simultaneous nonadaptive tests of Voss (1988). The approach is similar to that used by Wang and Voss (2003) to construct adaptive confidence intervals, but testing is simpler because one can use the same denominator for all statistics. Step-down tests also have a clear power advantage over simultaneous confidence intervals and analogous single-step tests, as is demonstrated theoretically and assessed via simulation.

Key words and phrases: Closed test, effect sparsity, factorial design, step-down test, stochastic ordering.