A proposed method of identifying significant effects in unreplicated factorial experiments

Abstract

In many areas of research/ production, a lot of factors are combined to obtain a desired product. To be able to analyze which factors (or combinations of factors and at what level) are significant, the experiment has to be replicated. For economic or practical reasons, it may not be feasible to perform the experiment more than once therefore unreplicated factorial designs are often employed. This is especially true in the field of Medicine, Pharmacy and Industrial production units. The traditional method of analysis of variance (ANOVA) cannot be employed in unreplicated factorial designs, therefore many methods have been proposed in literature. In this paper, a new method of analyzing unreplicated factorial designs is proposed and was compared with some of the existing methods. The four existing methods considered were: Lenth, Berk and Picard, Juan and Pena, and Dong. The comparison was performed using Monte Carlo simulation method. The criteria used in evaluating the performances of the methods are Power and Individual Error Rate (IER). Using these criteria of evaluation, the results showed that on overall performance, Dong method is the best among the four existing methods considered and was closely followed by Berk and Picard, Lenth, then Juan and Pena methods in that order. It was also found that not only is the proposed method simpler to compute, it competed favourably with Dong and even performed better than all the others when IER is used for assessment.