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

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 of polynomials for empirical quantitative modelling of treatment effects. The example analyses cover experiments with a single quantitative level factor, experiments with mixtures of quantitative and qualitative level factors, polynomial regression designs with two quantitative level factors, split‐plot designs with quantitative level factors and repeated‐measures designs with correlated data and a quantitative treatment response over time. Modern mixed model computer software for routine analysis of 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.