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The analysis of unreplicated factorial experiments from a geometric perspective

The author investigates the analysis of unreplicated factorial experiments from a geometric perspective. He considers more specifically a (k + 1)‐run experiment used to estimate k orthogonal contrasts. He observes that once centered and scaled to unit length, the response vector can be viewed as a point on the unit sphere in the vector space spanned by the contrasts. In this context, a model selection procedure is equivalent to a partition of the unit sphere into regions corresponding to the different models considered. The author exploits this approach to gain useful insights into the analysis of such experiments.