Pseudofactors: normal use to improve design and facilitate analysis

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Pseudofactors are an inherently simple device to aid the construction and analysis of designed experiments. Although they were introduced over 50 years ago, they still puzzle many statisticians. After a historical introduction a worked example is used to demonstrate how pseudofactors are used to construct the design, to obtain the analysis-of-variance table and table of means and to calculate standard errors of contrasts. Then the algebraic and algorithmic roles of pseudofactors are explained and reviewed, with particular emphasis on Genstat. Finally, a section on standard designs shows how pseudofactors may be used to construct more efficient designs, and to give simpler or better analyses, than those recommended in the current literature.
Original languageEnglish
Pages (from-to)317-336
Number of pages20
JournalJournal of the Royal Statistical Society: Series C (Applied Statistics)
Issue number2
Publication statusPublished - 1992


  • analysis of variance
  • efficiency factor
  • factorial design
  • general balance
  • Genstat
  • lattice square
  • optimal designs
  • pseudofactor
  • square lattice


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