A tutorial on the statistical analysis of factorial experiments with qualitative and quantitative treatment factor levels

Abstract

Agronomic experiments are often complex and difficult to interpret, and the proper use of appropriate statistical methodology is essential for an efficient and reliable analysis. In this paper, the basics of the statistical analysis of designed experiments are discussed using real examples from agricultural field trials. Factorial designs allow for the study of two or more treatment factors in the same experiment, and here we discuss the analysis of factorial designs for both qualitative and quantitative level treatment factors. Where treatment factors have quantitative levels, models of treatment effects are essential for efficient analysis and in this paper we discuss the use experimental data is now readily available, and we demonstrate the use of two alternative software packages, the SAS package and the R language. The main purpose of the paper is to exemplify standard statistical methodology for routine analysis of designed experiments in agricultural research, but in our discussion we also provide some references for the study of more advanced methodology.factorial analysis, linear mixed models, polynomial regression, R, repeated-measures analysis, response surface models, SAS, split-plot analysis | INTRODUCTIONAgronomic experiments are often difficult and complex both to plan and to execute and may depend on many factors that can affect both efficiency and reliability. They are usually expensive and may sometimes take many years to accomplish. In addition, agronomic experiments are typically subject to high background variability due to effects such as fertility trends in fields or initial weight differences between animals or year-to-year variability in weather as well as to the high natural variability of biological and agronomic systems. wileyonlinelibrary.com/journal/jac | 1 the aims of the experiment and produces accurate and efficient information that provides a simple and parsimonious description of the results while still taking proper account of the error structure of the design. A properly chosen analysis will provide not only a full summary of the observed data but will also give additional insight into the effects of the treatments on the system under study.The focus of this paper is on designed experiments with treatment structures that can be modelled by polynomial regression methods. All the experiments considered are comparative, meaning that the focus is exclusively on comparisons between treatments in the same experiment (Bailey, 2008;Giesbrecht & Gumpertz, 2004;Hinkelmann & Kempthorne, 1994). Polynomial regression is a standard linear model methodology that fits naturally within the standard analysis of variance. We will show how modern mixed model computer software can be used for the routine analysis of blocked experiments based on a range of block and treatment structures, including designs with repeated observations on the same experimental units.The paper does not explicitly discuss the design of experiments, but it will be assumed that the example data sets have been col...

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