Step-up test with a single cutoff for unreplicated orthogonal designs

This article presents a simplified means of controlling the experiment-wise risk of declaring too many effects active when analyzing an unreplicated orthogonal design. The method begins by assuming a lower bound on the number of null effects. The regression method of backward elimination is followed, comparing each F statistic with a common critical value, until the first statistically significant outcome. By using a single critical value, the method is simpler than the approach of Langsrud and Naes (1998) and Venter and Steel (1998) and is sometimes more powerful. Simulation is used to demonstrate the actual risk of Type I errors and power under various configurations of the true regression coefficients.