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Wednesday, January 16, 2013

Design of experiments via factorial designs

Authors: Jason Bourgeois, Michael Kravchenko, Nicholas Parsons, Andrew Wang
Stewards: Jocelyn Anleitner, Stephanie Combs, Diane Feldkamp, Heeral Sheth
Revised: 11/26/07

Factorial design is an important method to determine the effects of multiple variables on a response. Traditionally, experiments are designed to determine the effect of ONE variable upon ONE response. R.A. Fisher showed that there are advantages by combining the study of multiple variables in the same factorial experiment. Factorial design can reduce the number of experiments one has to perform by studying multiple factors simultaneously. Additionally, it can be used to find both main effects (from each independent factor) and interaction effects (when both factors must be used to explain the outcome). However, factorial design can only give relative values, and to achieve actual numerical values the math becomes difficult, as regressions (which require minimizing a sum of values) need to be performed. Regardless, factorial design is a useful method to design experiments in both laboratory and industrial settings.
Factorial design tests all possible conditions. Because factorial design can lead to a large number of trials, which can become expensive and time-consuming, factorial design is best used for a small number of variables with few states (1 to 3). Factorial design works well when interactions between variables are strong and important and where every variable contributes significantly.

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