The analysis of location and dispersion effects in unreplicated 2(k) factorial experiments

If an experiment takes place in the early stages of a research process, the purpose is often to quickly and efficiently screen or identify factors or interactions that significantly impact a response variable. These types of experiments are referred to as screening experiments. Factorial and fractional factorial experiments are commonly used as screening experiments because they allow for the simultaneous investigation of a large number of factors with relatively few experimental runs. If the resources available for the experiment are limited, the experiment may not contain replicates.; Screening experiments have historically been used to identify location effects or effects that influence the mean of a response variable. Hamada and Balakrishnan (1998) give an extensive overview of many existing methods for the identification of location effects. Loughin and Noble (1997) propose a permutation-based approach for the identification of active effects that appears to perform better than most existing methods when there are a large number of active effects relative the number of experimental runs. The large sample properties of their test procedure is investigated. In addition, four large sample approximations are presented and empirically compared to Loughin and Noble's permutation procedure.; More recently, due in part to the incorporation of Taguchi-type philosophies into experimentation, screening experiments have been used to identify dispersion effects, or effects that influence the variance of a response variable. Brenneman and Nair (2001) give an overview of existing dispersion testing methods. In addition, McGrath and Lin (2001) find that two unidentified location effects may cause a spurious dispersion effect and state that additional replication is necessary to identify the true cause of the disturbance in the response variable. A procedure is developed under an additive variance model which allows for the separation of location effects from dispersion effects without the need for additional experimentation. More importantly, it is shown that masking of an active dispersion effect may occur and unlike existing methods, the proposed procedure is robust to this phenomenon. A simulation study is used to compare the proposed procedure with commonly cited procedures.