A proposed method of identifying significant effects in unreplicated factorial experiments

B. B. Adeleke ,Bola Adijat Ibraheem

doi:10.28919/jmcs/4049

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.

Highlights

Experimentation is one of the most common activities that people engage in
The traditional method of analysis of variance (ANOVA) cannot be employed in unreplicated factorial designs, many methods have been proposed in literature
The criteria used in evaluating the performances of the methods are Power and Individual Error Rate (IER)

Summary

INTRODUCTION

Experimentation is one of the most common activities that people engage in. It covers a wide range of applications from household work like food preparation to technological innovation in material, science, agriculture, engineering etc. When there is no estimate for experimental error, the higher order interactions are often sacrificed for the estimate of error term, which are used for computing the required statistics in testing for the significance of the design factors. There is no estimate for experimental error, so the higher order interactions are often sacrificed for the estimate of error term, which are used for computing the required statistics in testing for the significance of the design factors. Because experimenters always consider as many factors as possible in a screening experiment, unreplicated fractional designs usually are saturated. Some existing methods of identification of significant effect in unreplicated designs and the proposed method were discussed in section two while data simulation and empirical comparison of the methods were given in section three and section four was on discussions of results and conclusion

PRELIMINARIES

Methods for identifying Active Location Effects

OF RESULTS AND CONCLUSION