What is a factorial design

In a factorial design, each variable (factor) is investigated at fixed levels  

In a two-level factorial design, each variable can take two values. For continuous variables, this will signify a low level and a high level. For discrete variables, this wiU signify the alternatives. In a three-level factorial design, three different levels of each variable is investigated, etc. 

A complete factorial design contains aU possible settings of the experimental variables. A factorial design in which k factors are studied at r levels wiU thus contain z different experimental runs A two-level factorial design with k factors contains 2 runs. 

It is seen that the number of individual experimental runs increases rapidly with an increasing number of factors, and even more rapidly when more than two levels are used. 

The arrangement of experimental runs in a factorial design makes it possible to use each observed response more than once. Each result is actualfy used in combinations with the other results to compute an average response, all main effects, all two-factor interaction effects. all multi-factor interaction effects. This means that each individual experimental run is equalfy important to the overaU result. 

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