Statistical Elements of a Successful Farm-scale Trial
Abstract
Growers and advisers increasingly run large strip trials on their own paddocks, but the rules used to design them come from small-plot research. We simulated strip trials on a spatially autocorrelated field, varying trial length (L), replication (r), randomised or systematic allocation, and long-strip or stacked layout, for a nitrogen response that was uniform or varied across within-field pseudo-environments (PEs). Analyses of strip-plot means and of yield pixels were first checked for Type I error, and designs were then compared by the smallest response that a valid analysis detects with 80% power. Follow-up runs added gaps, unequal strip lengths, trends, spatially varying responses and alternative field structures; more than 3 million models were fitted. Treating pixels as independent replicates gave false positives in 32-40% of null trials. Replication was the strongest design lever: the detectable response scaled as r−0.60 to r−1.02 but only as L−0.45 or more slowly, and at equal plot area more, shorter replicates won all 66 comparisons. With complete data, strip means with an autoregressive residual were the most precise analysis; when strips contained gaps, pixel-level spatial models with a strip effect halved the detectable response, while the spatial analysis of strip means became liberal. For PE-varying responses, spatial PE models detected per-PE effects 33-46% smaller than PE means without a spatial term. Randomisation did not improve precision but kept tests valid (systematic allocation: Type I error up to 23%), whereas systematic allocation gave more accurate response maps. The results are condensed into a design table and a detectable-gain chart for use before a trial is sown.
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BibTeX
@misc{cao2026statistical,
title = {{Statistical Elements of a Successful Farm-scale Trial}},
author = {Zhanglong Cao and Suman Rakshit and Barbara Kachigunda and Julia Easton and Mark Gibberd},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38297},
eprint = {2610.38297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38297},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Statistical Elements of a Successful Farm-scale Trial
AU - Zhanglong Cao
AU - Suman Rakshit
AU - Barbara Kachigunda
AU - Julia Easton
AU - Mark Gibberd
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38297
UR - https://arxiv.org/abs/2610.38297
AB - Growers and advisers increasingly run large strip trials on their own paddocks, but the rules used to design them come from small-plot research. We simulated strip trials on a spatially autocorrelated field, varying trial length (L), replication (r), randomised or systematic allocation, and long-strip or stacked layout, for a nitrogen response that was uniform or varied across within-field pseudo-environments (PEs). Analyses of strip-plot means and of yield pixels were first checked for Type I error, and designs were then compared by the smallest response that a valid analysis detects with 80% power. Follow-up runs added gaps, unequal strip lengths, trends, spatially varying responses and alternative field structures; more than 3 million models were fitted. Treating pixels as independent replicates gave false positives in 32-40% of null trials. Replication was the strongest design lever: the detectable response scaled as r^−0.60 to r^−1.02 but only as L^−0.45 or more slowly, and at equal plot area more, shorter replicates won all 66 comparisons. With complete data, strip means with an autoregressive residual were the most precise analysis; when strips contained gaps, pixel-level spatial models with a strip effect halved the detectable response, while the spatial analysis of strip means became liberal. For PE-varying responses, spatial PE models detected per-PE effects 33-46% smaller than PE means without a spatial term. Randomisation did not improve precision but kept tests valid (systematic allocation: Type I error up to 23%), whereas systematic allocation gave more accurate response maps. The results are condensed into a design table and a detectable-gain chart for use before a trial is sown.
ER -