Comparison Of Some Methods For Analyzing Data From Unreplicated Factorial Experiments

Factorial designs are very popular in industrial experiments because of their high efficiency. In unreplicated fractional factorial experiments, there is no reliable estimate of the variance of the contrast, so t-test and F-test can not be used to identify active effect.Since the 1980's, many objective methods for analyzing unreplicated factorial designs have appeared on the premise of effect sparsity. This paper gives an introduction of Lenth Method, Dong Method, Step-down Lenth Method and some methods suggested by Venter and Steel in 1996 and 1998. Enlightened by Step-down Lenth Method, we propose Step-down Dong Method. At the last part of this paper, using computer, we perform a simulation study to compare all these methods and find that when the hypothesis of effect sparsity is true, Step-down Dong Method works well, but if the practitioner is not quite sure of the effect sparsity, the sequential scaling step-up method proposed by Venter and Steel in 1998 is a good alternative.