Applied Statistics Lesson of the Day – Fractional Factorial Design and the Sparsity-of-Effects Principle
April 9, 2014 Leave a comment
Consider again an experiment that seeks to determine the causal relationships between factors and the response, where . Ideally, the sample size is large enough for a full factorial design to be used. However, if the sample size is small and the number of possible treatments is large, then a fractional factorial design can be used instead. Such a design assigns the experimental units to a select fraction of the treatments; these treatments are chosen carefully to investigate the most significant causal relationships, while leaving aside the insignificant ones.
When, then, are the significant causal relationships? According to the sparsity-of-effects principle, it is unlikely that complex, higher-order effects exist, and that the most important effects are the lower-order effects. Thus, assign the experimental units so that main (1st-order) effects and the 2nd-order interaction effects can be investigated. This may neglect the discovery of a few significant higher-order effects, but that is the compromise that a fractional factorial design makes when the sample size available is low and the number of possible treatments is high.