# Statistics, metadata and data publication

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Experimental units, randomisation, blocking, mixed models, effect sizes, multiplicity and machine-readable data publication.

In brief

Experimental units, randomisation, blocking, mixed models, effect sizes, multiplicity and machine-readable data publication.

## Experimental unit

The biological experimental unit is the smallest independently assigned unit. Multiple leaves from one plant are subsamples, not independent plants. Plants sharing one reservoir may not be independent for a nutrient-solution treatment; reservoir or run can become the true treatment unit.

## Design controls

- random assignment to position and treatment;
- blocking by cycle and relevant spatial factor;
- blinded sample coding for laboratory and sensory analysis;
- predefined exclusion and deviation rules;
- power analysis updated from pilot variance;
- effect size and confidence interval reported with p-values.

## Example mixed model

 STAT-1 y = μ + t r e a t m e n t + p o s i t i o n + t r e a t m e n t × c u l t i v a r + c y c l e ( r a n d o m ) + ε y=\mu+\mathrm{treatment}+\mathrm{position}+\mathrm{treatment}\times\mathrm{cultivar}+\mathrm{cycle}_{(\mathrm{random})}+\varepsilon y = μ + treatment + position + treatment × cultivar + cycle ( random ) ​ + ε Example structure; the final model follows the actual experimental unit and design.

**Explanation**The model separates treatment, position, cultivar and cycle effects so a treatment is not credited for variation produced elsewhere.

## Multiple outcomes

Primary outcomes are declared before analysis. Secondary chemistry and sensory endpoints are labelled and multiplicity is controlled where inferential claims are made.

Measurement uncertainty and precision terminology are declared separately from biological variation. Repeatability and reproducibility are not treated as synonyms. [R38] [R46] [R50]

## Data package

Every report links raw data, processed data, analysis code, data dictionary, protocol, deviations and checksums. Metadata follow MIAPPE concepts and FAIR principles. [R23] [R24]

## References

- [R23] Papoutsoglou, E. A. et al. (2020). Enabling reusability of plant phenomic datasets with MIAPPE 1.1. *New Phytologist*. https://doi.org/10.1111/nph.16544
- [R24] Wilkinson, Mark D. et al. (2016). The FAIR Guiding Principles for scientific data management and stewardship. *Scientific Data*. https://doi.org/10.1038/sdata.2016.18
- [R38] Joint Committee for Guides in Metrology (2008). Evaluation of measurement data — Guide to the expression of uncertainty in measurement. *JCGM 100:2008*. https://doi.org/10.59161/JCGM100-2008E
- [R46] Heckert, N. Alan; Filliben, James J.; Croarkin, C. M.; Hembree, B.; Guthrie, William F.; Tobias, P.; Prinz, J. (2002). NIST/SEMATECH e-Handbook of Statistical Methods. *NIST Handbook 151*.
- [R50] International Organization for Standardization (2025). ISO 5725-2:2025 Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method. *ISO*.