Design of experiments with multiple independent variables: a resource management perspective on complete and reduced factorial designs

Abstract

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 whether research questions are framed as main effects or simple effects; whether and which effects are aliased (confounded) in a particular design; the number of experimental conditions that must be implemented in a particular design and the number of experimental subjects the design requires to maintain the desired level of statistical power; and the costs associated with implementing experimental conditions and obtaining experimental subjects. In this article 4 design options are compared: complete factorial, individual experiments, single factor, and fractional factorial. Complete and fractional factorial designs and single-factor designs are generally more economical than conducting individual experiments on each factor. Although relatively unfamiliar to behavioral scientists, fractional factorial designs merit serious consideration because of their economy and versatility.

Figure 1

Costs of different experimental design options when per-subject costs exceed per-condition overhead costs. Total costs are computed with per-condition costs fixed at $1.

Figure 2

Costs of different experimental design options when per-condition overhead costs exceed per-subject costs. Total costs are computed with per-subject costs fixed at $1.

Figure 3

Partial output from SAS PROC GLM for simulated Resolution III data set.