Statistical analysis of comparative experiments based on large strip on-farm trials

Abstract

Statistical methods used for small plot analyses are unsuitable for large-scale on-farm experiments because they fail to take into account the spatial variability in treatment effects within paddocks. Several new methods have recently been proposed that are inspired by geostatistical analyses of spatially-varying treatment effects, which are typical for site-specific crop management trials with quantitative treatments. However, these methods do not address the objective of comparative experiments, where the overall assessment of treatments’ performance is of interest. Moreover, most biometricians, who routinely analyse data from field trials, are either unfamiliar with the new geostatistical techniques or reluctant to include these in their regular analytical toolkits due to the unavailability of easy-to-use software tools. The linear mixed model is widely used for analysing small plot field trials because it is extremely versatile in modelling spatial and extraneous variability and is accessible through user-friendly software implementation. Motivated by comparative experiments, conducted in large strip trials using qualitative treatment factors, and yield data obtained from harvest monitor, we propose a linear mixed effects model for determining the best treatment at both local and global spatial scales within a paddock, based on yield predictions and profit estimates. To account for the large spatial variation in on-farm strip trials, we divide the trial into smaller regions or pseudo-environments (PEs), each containing at least two replicates. We propose two approaches for creating these PEs. In the presence of appropriate spatial covariates, a clustering method is proposed; otherwise, the trial area is stratified into equal-sized rectangular blocks using a systematic partitioning scheme. PEs are used to estimate the treatment effects by incorporating treatment-by-PE interactions in linear mixed effects models. The optimum treatment within each PE is found by either comparing the best linear unbiased predictions solely or incorporating profit and comparing economic performance. To illustrate the applicability of our method, we have analysed two large strip trials conducted in Western Australia.