Decomposition tables for experiments. II. Two–one randomizations

C. J. Brien*, Rosemary Anne Bailey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.

Original languageEnglish
Pages (from-to)3164-3190
Number of pages27
JournalAnnals of Statistics
Issue number5
Publication statusPublished - Oct 2010


  • Analysis of variance
  • Balance
  • Decomposition table
  • Design of experiments
  • Efficiency factor
  • Intertier interaction
  • Multiphase experiments
  • Multitiered experiments
  • Orthogonal decomposition
  • Pseudofactor
  • Structure
  • Tier


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