MSc Statistics Defence: Pooling Methods and Similarity Measures for Fractional Factorial Designs in the Presence of an Auxiliary Variable

CANDIDATE:    ANDREW PORTER

 It is well-known that the standard mean squared error obtained from a half fractional factorial provides a conservative estimate of the error variance, which can affect tests for active main effects. This thesis proposes two new pooling methods, which use a full factorial auxiliary variable to adjust the MSE for the half fractional factorial response and compares them to two existing univariate methods. However, the utility of these methods depends on the relationship between the responses. Consequently, three similarity measures are proposed to develop a diagnostic tool when the new pooling methods may be beneficial. Analysis of four empirical factorial experiments using the four pooling methods is performed to inform the design of a simulation study. Through this simulation study, the pooling methods and utility of the similarity measures are evaluated. Finally, a procedure for calculating Monte Carlo p-values is developed for one of the new pooling methods.