Analysis of Dispersion Effects in Unreplicated Factorial Designs

Abstract: Methods for estimating and testing hypotheses of dispersion effects in two-level unreplicated factorial designs are studied. Under a particular = normal model, some linear combinations of the response variables are constructed in order to make a simple inference. One method uses an F-test after eliminating all but one dispersion parameter, while another method is based on dependencies between linear combinations.

The consequences of performing fractional experiments are discussed. The problems that arise in this case are treated either by working with several variance ratios or by using the covariance structure. Often, the quality of the methods differ. It might even happen that some methods work while others are not possible to construct.

Comparative calculations of power functions are carried out and illustrations from industry are presented.