Optimum experimental design for Free-Air Carbon dioxide Enrichment (FACE) studies

This article presents the logical reasoning underlying the optimal design o f an experiment. We used Free-Air Carbon dioxide Enrichment (FACE) experime nts to illustrate this trade-off as such experiments are particularly costl y. On a theoretical basis, two-way nested designs and split-plot designs ha ve similar power in testing carbon dioxide (CO2) main effects. If researche rs have the choice of adding two replicate rings or two control plots to th eir experiment, our results show that both options provide a substantial ga in in statistical power, with a slightly greater gain in the former case an d at reduced financial cost in the latter. The former option, however, prov ides an insurance against possible ring failure. On an empirical basis, we analysed a preliminary FACE photosynthesis datase t 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 significa nt main effect of GROWTH. Power analysis was used to understand why the GRO WTH main effect was not significant. The minimum detectable difference betw een treatment means that we calculated for GROWTH in this experiment was 4. 04 mu mol CO2 m(-2) s(-1) for a statistical power of 0.90, whereas the obse rved difference was 0.16 mu mol 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 obtai n a split-plot design that provides a powerful test of interaction between treatment factors; (ii) add control plots, unless financial constrictions d isallow for necessary personnel; (3) pool the data of FACE experiments cond ucted in comparable ecosystems (e.g. forests or grasslands), with two rings per treatment level at each site.