General balance: artificial theory or practical relevance?

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


If an experiment has orthogonal block structure then linear combinations of the data can be allocated to various strata, in such a way that combinations in different strata are uncorrelated and all normalized combinations in a single stratum have the same variance. The analysis of the experiment is computationally and conceptually simple if the design has the property of general balance, introduced by Nelder: that is, there is an orthogonal basis for the space of treatments, such that, in any stratum in which they are both estimable, the estimators of any pair of basis elements are uncorrelated.

More recent results show that general balance is related to commutativity of certain matrices. It is possible that neither computational simplicity nor abstract commutativity has anything to do with practical experiments in these days of high computer power. A contrary argument says that general balance aids interpretation and that the design which is generally balanced with respect to meaningful contrasts may be superior to a technically optimal design.
Original languageEnglish
Title of host publicationProceedings of the International Conference on Linear Statistical Inference LINSTAT '93
EditorsT. Cali'nski, R. Kala
Place of PublicationDordrecht
PublisherKluwer Academic Publishers
Number of pages14
ISBN (Print)0 7923 3136 2
Publication statusPublished - 1994

Publication series

NameMathematics and its Applications


  • basic contrasts
  • efficiency
  • general balance
  • incomplete-block designs
  • optimality
  • orthogonal block structure
  • strata


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