The design and structure of multitiered experiments

Dr Chris Brien

Multitiered experiments ( are characterized by involving more than one randomization and so are more complicated than standard experimental designs found in textbooks, as the latter involve only a single randomization. A particular application is to two-phase experiments where material from a first experiment is not finished with once it has been produced but must be collected and kept over for further processing or experimentation. One example is a grape growing experiment where the grapes are to be harvested, after which they are taken to a winery to be processed into wine prior to evaluation in a sensory experiment. Here an experimental design is required for the grape-growing experiment and a second design, that accommodates the first design, is needed for the sensory experiment. It is an example of a wider class of experiments that consist of a laboratory/measurement phase subsequent to an initial phase. Other types of experiments that are multitiered include superimposed, some plant and grazing experiments

The different types of multiple randomization that can occur in multitiered experiments have been identified and described by Brien and Bailey (2006) and they develop randomization diagrams for exhibiting the randomizations. The structure of multitiered experiments and the conditions under which they are balanced have been described by Brien and Bailey (2009, 2010). Currently, general principles for the design of multiphase experiments that involve a laboratory/measurement phase subsequent to an initial phase are being developed.


Prof. R. A. Bailey, School of Mathematical Sciences, Queen Mary, University of London, UK
Dr. B. D. Harch, CSIRO Mathematical and Information Sciences, Qld, Australia
Dr R. L. Correll, Rho Environmetrics, SA, Australia


Brien, C. J. & Bailey, R. A. (2006) Multiple randomizations (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology)68, 571-609.

Brien, C. J. & Bailey, R. A. (2009) Decomposition tables for multitiered experiments. I. A chain of randomizations. The Annals of Statistics, 36(6B): 4184 -- 4213.

Brien, C. J. & Bailey, R. A. (2010) Decomposition tables for multitiered experiments. II. Two-one randomizations. Accepted for publication in The Annals of Statistics.

Areas of study and research

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