Fractional factorial designs are widely used experimental plans for identifying important factors in screening studies where many factors are involved. Traditionally, Plackett-Burman (PB) and related designs are employed for in such studies because of their cost eﬃciencies. The caveat with the use of PB designs is that interactions among factors are implicitly assumed to be non-existent. However, there are many practical situations where some interactions are signiﬁcant and ignoring them can result in wrong statistical inferences, including biased estimates, missing out on important factors and detection of spurious factors. We reanalyze data for three chemical experiments using the Hamada and Wu’s method and show that we are able to identify signiﬁcant interactions in each of these chemical experiments and improve the overall ﬁt of the model. In addition, we analyze the data using a Bayesian approach that conﬁrms our ﬁndings. In both approaches, graphical tools are employed along with easily available software for analysis.

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Department of Statistics, UCLA (4) Biostatistics (3)

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Medicine and Health Sciences (3) Physical Sciences and Mathematics (3)

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## Scholarly Works (9 results)

When there is interest to study n chemicals using x dose levels each, factorial designs that require xn treatment groups have been put forward as one of the valuable statistical approaches for hazard assessment of chemical mixtures. Exemplary applications and cost-eciency comparisons of full factorial designs and regular fractional factorial designs in toxicity studies can be found in Nesnow et al. (1995), Narotsky et al. (1995), and Groten et al. (1996,1997). We introduce nonregular fractional factorial designs and show their bene�ts using two studies reported in Groten et al. (1996). Study 1 shows nonregular designs can provide the same amount of information using 75% of the experimental costs required in a regular design. Study 2 demonstrates nonregular designs can additionally estimate some partially aliased e�ects, which cannot be done using regular designs. We also provide a statistical method to evaluate the quality of an assumption made by experts in Study 2 of Groten et al. (1996).

When there is interest to study n chemicals using x dose levels each, factorial designs that require xn treatment groups have been put forward as one of the valuable statistical approaches for hazard assessment of chemical mixtures. Exemplary applications and cost-eﬃciency comparisons of full factorial designs and regular fractional factorial designs in toxicity studies can be found in Nesnow et al. (1995), Narotsky et al. (1995), and Groten et al. (1996,1997). We introduce nonregular fractional factorial designs and show their beneﬁts using two studies reported in Groten et al. (1996). Study 1 shows nonregular designs can provide the same amount of information using 75% of the experimental costs required in a regular design. Study 2 demonstrates nonregular designs can additionally estimate some partially aliased eﬀects, which cannot be done using regular designs. We also provide a statistical method to evaluate the quality of an assumption made by experts in Study 2 of Groten et al. (1996).

Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. The traditional analysis focuses on main e�ffects only. Hamada and Wu (1992) went beyond the traditional approach and proposed an analysis strategy to demonstrate that some interactions could be entertained and estimated beyond a few significant main effects. Their groundbreaking work stimulated much of the recent developments in design criterion creation, construction and analysis of nonregular designs. This paper reviews important developments in optimality criteria and comparison, including projection properties, generalized resolution, various generalized minimum aberration criteria, optimality results, construction methods and analysis strategies for nonregular designs.