Affiliation:
1. School of Agriculture Food and Wine, University of Adelaide Adelaide South Australia Australia
2. UniSA STEM University of South Australia Adelaide South Australia Australia
3. Luiz de Queiroz College of Agriculture (ESALQ) University of São Paulo Piracicaba São Paulo Brazil
Abstract
AbstractComparative experiments involve the allocation of treatments to units, ideally by randomization. This necessarily confounds treatment information with unit information, which we distinguish from the other forms of information blending, in particular aliasing and marginality. We outline a factor‐allocation paradigm for describing experimental designs with the aim of (i) exhibiting the confounding in a design, using analysis‐of‐variance‐like tables, so as to understand and evaluate the design and (ii) formulating a linear mixed model based on the factor allocation that the design involves. The approach exhibits the dispersal of treatments information between units sources, allows designers a choice in the strategy that they adopt for including block‐treatment interactions, clarifies differences between experiments, accommodates systematic allocation of factors, and provides a consolidated analysis of nonorthogonal designs. It provides insights into the process of designing experiments and issues that commonly arise with designs. The paradigm has pedagogical advantages and is implemented using the R package dae.
Subject
Statistics, Probability and Uncertainty,General Medicine,Statistics and Probability