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Factorial designs are often used in various industrial and sociologicalexperiments to identify significant factors and factor combinations that mayaffect the process response. In the statistics literature, several studies haveinvestigated the analysis, construction, and isomorphism of factorial andfractional factorial designs. When there are multiple choices for a design, itis helpful to have an easy-to-use tool for identifying which are distinct, andwhich of those can be efficiently analyzed/has good theoretical properties. Forthis task, we present an R library called IsoCheck that checks the isomorphismof multi-stage 2^n factorial experiments with randomization restrictions.Through representing the factors and their combinations as a finite projectivegeometry, IsoCheck recasts the problem of searching over all possiblerelabelings as a search over collineations, then exploits projective geometricproperties of the space to make the search much more efficient. Furthermore, abitstring representation of the factorial effects is used to characterize allpossible rearrangements of designs, thus facilitating quick comparisons afterrelabeling. We present several examples with R code to illustrate the usage ofthe main functions in IsoCheck. Besides checking equivalence and isomorphism of2^n multi-stage factorial designs, we demonstrate how the functions of thepackage can be used to create a catalog of all non-isomorphic designs, andsubsequently rank these designs based on a suitably defined ranking criterion.IsoCheck is free software and distributed under the General Public License andavailable from the Comprehensive R Archive Network.

IsoCheck: An R Package to check Isomorphism for Two-level Factorial Designs with Randomization Restrictions