Overview of research into the design and mixed model analysis of multitiered experiments
Brien (2017c) gives a review of the research conducted into the design and analysis of multiphase experiments, an important subclass of multitiered experiments. Two strands in the literature are of identified: experiments that are structure balanced and those that are unbalanced.
For structure balanced multitiered experiments, Brien and Bailey (2006) describe a number of types of randomization,. The series of papers Brien and Bailey (2009), Brien and Bailey (2010) and Bailey and Brien (2016) represent a complete theory for the analysis of multitiered experiments in which the allocations are in a chain.
For unbalanced experiments, Smith et al. (2001), Cullis et al. (2003), Smith et al. (2006), Smith et al., 2011 and Smith et al., 2015 have developed methods for the design and analysis of early-stage plant breeding experiments that involve a large number lines.
Current research includes:
- An investigation of the principles and laws applicable to nonorthogonal multiphase experiments.
- The derivation of a theory for the analysis of multitiered experiments involving two-one randomizations.
- Considerations in the allocation of treatment replicates.
- The randomization analysis of multitiered experiments involving a chain of randomizations.