Optimum experimental design for Free‐Air Carbon dioxide Enrichment (FACE) studies
Bibliographic record
Abstract
Summary This article presents the logical reasoning underlying the optimal design of an experiment. We used Free‐Air Carbon dioxide Enrichment (FACE) experiments to illustrate this trade‐off as such experiments are particularly costly. On a theoretical basis, two‐way nested designs and split‐plot designs have similar power in testing carbon dioxide (CO2) main effects. If researchers have the choice of adding two replicate rings or two control plots to their experiment, our results show that both options provide a substantial gain in statistical power, with a slightly greater gain in the former case and at reduced financial cost in the latter. The former option, however, provides an insurance against possible ring failure. On an empirical basis, we analysed a preliminary FACE photosynthesis dataset collected at Duke University. The experiment was designed as a split‐plot design to test the effects of growth environment (GROWTH) and measurement CO2 concentration (MEAS) on photosynthetic rates of loblolly pine. Although a significant effect of MEAS was observed, we failed to detect a significant main effect of GROWTH. Power analysis was used to understand why the GROWTH main effect was not significant. The minimum detectable difference between treatment means that we calculated for GROWTH in this experiment was 4.04 μmol CO2 m−2 s−1 for a statistical power of 0.90, whereas the observed difference was 0.16 μmol CO2 m−2 s−1. Our recommendations for the design of FACE experiments are: (i) consider a second treatment factor with many levels within each ring in order to obtain a split‐plot design that provides a powerful test of interaction between treatment factors; (ii) add control plots, unless financial constrictions disallow for necessary personnel; (3) pool the data of FACE experiments conducted in comparable ecosystems (e.g. forests or grasslands), with two rings per treatment level at each site.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.049 | 0.089 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".