Minimum aberration designs are obtained for two types of mixed-level fractional factorial: (i) (s) × s factorial, and (ii) (s1) × (s2) × s factorial, where s is any prime or prime power, and r, r1, r2 and n are positive integers. Projective geometric tools are employed to find the wordlength pattern of a given design in terms of that of its complementary set. Many useful designs are found

Marketers have recently begun to embrace complex experimental designs for marketing and advertising testing. Full-factorial, fractional-factorial and Plackett–Burman designs have given marketers new statistical tools to increase the speed, power, and profitability of their testing programs. This case study shows how well constructed and managed experimental designs offer marketing professionals...

An investigator who plans to conduct an experiment with multiple independent variables must decide whether to use a complete or reduced factorial design. This article advocates a resource management perspective on making this decision, in which the investigator seeks a strategic balance between service to scientific objectives and economy. Considerations in making design decisions include wheth...

We consider Markov basis arising from fractional factorial designs with threelevel factors. Once we have a Markov basis, p values for various conditional tests are estimated by the Markov chain Monte Carlo procedure. For designed experiments with a single count observation for each run, we formulate a generalized linear model and consider a sample space with the same sufficient statistics to th...

We consider Markov basis arising from fractional factorial designs with threelevel factors. Once we have a Markov basis, p values for various conditional tests are estimated by the Markov chain Monte Carlo procedure. For designed experiments with a single count observation for each run, we formulate a generalized linear model and consider a sample space with the same sufficient statistics to th...

By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular, it reduces to the minimum aberration criterion for ...

When there is interest to study n chemicals using x dose levels each, factorial designs that require x(n) 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 Nesn...

We consider the design and analysis of multi-factor experiments using fractional factorial incomplete designs within potential outcome framework. These are particularly useful when limited resources make running a full infeasible. connect our design-based methods to standard regression methods. further motivate usefulness these in observational studies, where certain treatment combinations may ...