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The analysis of unreplicated factorial experiments from a geometric perspective
Author(s) -
Miller Arden E.
Publication year - 2003
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316089
Subject(s) - perspective (graphical) , factorial , partition (number theory) , context (archaeology) , point (geometry) , mathematics , factorial experiment , unit vector , unit sphere , unit (ring theory) , space (punctuation) , computer science , combinatorics , statistics , geometry , mathematical analysis , paleontology , biology , mathematics education , operating system
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.