An Adaptation of the Bergman–Hynén Test for Dispersion Effects in Unreplicated Two-Level Factorial Designs When the Location Model May Be Incorrect

Abstract

In the analysis of unreplicated two-level factorial experiments, it is well established that pairs of active location effects that are not identified as active can cause a disturbance in the data that interferes with standard tests and estimates for dispersion effects. An amendment to the dispersion-effect test of Bergman and Hynén (1997) is proposed to make it robust against confounding by location effects. The cost of this robustness is only one degree of freedom from the numerator and denominator of the reference F distribution. Simulations demonstrate a newfound problem with the Bergman–Hynén test and show that the proposed amendment fixes this problem.