Randomization-based models for multitiered experiments: I. A chain of randomizations

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6 Citations (Scopus)


We derive randomization-based models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.
Original languageEnglish
Pages (from-to)1131-1164
Number of pages34
JournalAnnals of Statistics
Issue number3
Early online date11 Apr 2016
Publication statusPublished - Jun 2016


  • Analysis of variance
  • Expected mean square
  • Mixed model
  • Multiphase experiments
  • Multitiered experiments
  • Randomization-based model
  • REML
  • Structure
  • Tier


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