| name | fcr-data-analysis |
| description | Use when executing and reporting the statistical analysis for a Field Crops Research (FCR) manuscript — mixed models for multi-environment, block-design, and split-plot designs, genotype-by-environment (G×E) and stability analysis, estimated marginal means with SED/LSD, and crop-model evaluation. FCR requires data analysed with appropriate statistics that match the design and address the objectives. Guides analysis norms; it does not fabricate results. |
Data Analysis (fcr-data-analysis)
FCR requires that data be analysed with appropriate statistics and that results be concise and
address the objectives. For field-crop work that almost always means mixed models that respect
the design (blocks, split-plots, environments) — not a one-way ANOVA on pooled plots. Analysis
execution lives here; design decisions live in fcr-experimental-design.
When to trigger
- Building the analysis and results section from trial or modelling data
- A reviewer asked for the correct error structure, G×E modelling, or proper means separation
- Reconciling main effects with interactions across environments
- Evaluating a crop model against observations
Analysis norms FCR expects
- Match the model to the design. Use a linear mixed model with the error structure implied by
the layout: blocks, whole-plot vs. sub-plot errors (split-plot), environment as a factor, and
correct random effects (e.g., environment, block, genotype-within-environment). A wrong error
term inflates significance.
- G×E done properly. Test and interpret genotype/treatment × environment; where ranking matters,
use Finlay–Wilkinson, AMMI, or GGE biplot stability analysis. Report whether the
treatment effect is consistent or environment-dependent.
- Means separation the right way. Report estimated marginal (adjusted) means with SE / SED
or LSD at a stated α; avoid bare means with significance stars and avoid over-using multiple-range
tests on quantitative factors — fit a response curve instead (N, water, density).
- Report uncertainty and effect size. Give the magnitude of the agronomic effect (e.g., kg ha⁻¹,
% yield change) with intervals, and its agronomic meaning — not just p-values.
- Check assumptions. Residual diagnostics, variance homogeneity across environments, and
transformation/weighting where needed; consider spatial models for heterogeneous fields.
- Meta-analysis. If synthesising published trials, use proper meta-analytic models (effect sizes,
heterogeneity, weighting) — not vote-counting.
Crop-model evaluation
- Report fit statistics on independent validation data: RMSE, nRMSE, mean bias, modelling
efficiency (EF), and (with care) R²; show observed-vs-simulated with the 1:1 line.
- Separate calibration from validation; state cultivar coefficients and model version.
Reproducibility while you work
- One analysis script regenerates every table and figure from the (raw or constructed) data.
- Set and report seeds for any stochastic/bootstrap/simulation step; pin software/package versions.
- Keep table/figure numbers matched to script outputs (supports the data-availability deposit — see
fcr-reporting-and-data-policy).
Error-structure decision table (match the model to the layout)
The fastest way a methods reviewer rejects an analysis is a mismatch between the test and the trial's
blocking structure. Read off the error terms the design implies.
| Design | Fixed effects | Random / error terms |
|---|
| RCBD, one environment | treatment | block |
| Split-plot | whole-plot factor, sub-plot factor, interaction | block; whole-plot error; sub-plot (residual) error |
| MET (RCBD per site) | treatment | environment, environment×treatment, block-in-environment |
| Alpha-lattice | treatment | replicate, incomplete-block-in-replicate |
| Repeated measures over time | treatment, time, interaction | plot (subject); within-plot correlation |
Worked analysis vignette (illustrative)
Illustrative; the inference logic matters, not the exact values. Take the split-plot MET above — a new
wheat cultivar vs. a check, 5 N rates, 8 environments, 4 blocks each. A naive one-way ANOVA on the
pooled plots tests cultivar against the residual and reports p < 0.001 for a 0.6 t ha⁻¹ advantage —
the classic inflated result: cultivar is a sub-plot factor, but the environment×cultivar interaction
is the right yardstick for a general claim. The mixed model (cultivar and N fixed; environment,
block-within-environment, and environment×cultivar random) shows the advantage is ~0.9 t ha⁻¹ at 3
high-N sites but ~0.1 t ha⁻¹ (n.s.) at the 2 low-rainfall sites — a real G×E.
Report adjusted means with SED per environment, fit an N response curve rather than pasting
a/b/c letters on the 5 rates, and frame the conclusion conditionally. Same data, opposite paper: the
second survives review because error structure and G×E are honored.
Anti-patterns
- One-way ANOVA on pooled plots, ignoring blocks/split-plot/environment structure
- Pseudoreplication: treating sub-samples within a plot as independent replicates
- Mean-separation letters (a/b/c) slapped on a quantitative dose — fit a curve
- Reporting significance without effect size, interval, or agronomic interpretation
- Pooling environments and hiding a strong G×E interaction
Output format
【Model】mixed model: fixed = ___, random = ___, error structure = ___
【G×E】tested? consistent vs. environment-dependent? stability method
【Means】adjusted means + SED/LSD at α; response curve where quantitative
【Effect size】magnitude (units) + interval + agronomic meaning
【Diagnostics】assumptions checked? spatial model if needed? [Y/N]
【Model eval (if any)】RMSE/nRMSE/EF on independent data
【Next】fcr-figures-and-tables
Supplementary resources
