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Keywords:

  • FACE;
  • optimal experimental design;
  • power analysis

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.