Optimal design for on-farm strip trials—systematic or randomised?

Context or problem

Randomised designs are often preferred over systematic designs by agronomists and biometricians. For on-farm trials, however, the choice may depend on the objective of the experiment. If the purpose is to create a prescription map of a continuous input for each plot in a grid covering a large strip trial, a systematic design may be a better choice, although it often attracts less discussion and attention.

Objective or research question

This study aims to evaluate the performance of systematic designs with geographically weighted regression (GWR) models in addressing spatial variation and estimating continuous treatment effects in large strip trials through numeric simulations.

Methods

A hierarchical model with spatially correlated random parameters is utilised to generate simulated data for various scenarios of large strip on-farm trials. The study employs GWR models to analyse the simulated data for two assumptions: a linear response and a quadratic response of yield to the treatment effects.

Results

With the assumption of a quadratic response, a systematic design is superior to a randomised design in terms of achieving lower mean squared errors (MSEs) with GWR. With the assumption of a linear response, the difference of MSE between a systematic design and a randomised design is not significant, regardless of the presence of spatial variation.

Conclusions

The findings highlight the superiority of systematic designs in producing smooth spatial maps of optimal input levels for quadratic response models in large strip trials, even when impacted by significant spatial variation. Additionally, we recommend selecting fixed bandwidths in GWR analysis based on the plot configurations used in experimental designs. For a large strip trial, to produce estimates of spatially-varying treatment effects across strips, a systemic design should be used as it allows us to obtain better estimates than those obtained from a randomised design in post-experiment statistical modelling.

Implications or significance

The findings offer practical recommendations for designing large strip trials. By drawing attention to the experiment’s main inferential purpose, this research contributes valuable insights for improving the efficacy and planning of large strip trials.