An augmented factorial design, which includes a standard factorial structure and an untreated control, has been frequently used in experimental studies of different disciplines, but data analysis is often inappropriate. Fractional compositional data analysis is also common in ecological studies, e.g., biomass allocation pattern analysis. There are several pitfalls of traditional analysis methods. For example, applying transformations for fractional data might distort the relationships among components, separately analyzing fraction or fraction ratio equations ignores the additivity constraint that all fractions remain non-negative and sum to 1, and it would be hard to give rigorous statistical tests. We will present an augmented factorial filed experiment on drip irrigation and nitrogen fertigation (DIF) in triploid Populus tomentosa plantations and show how to use appropriate ANOVA for stand growth and the Dirichlet regression model (DRM) approach for biomass allocation analysis.
Results/Conclusions
High irrigation significantly enhanced early stand growth, but additional N fertigation did not further improve early stand growth. Compared with traditional methods such as biomass ratio or allometric equation approaches, the DRM was directly fitted to biomass proportion data without any transformation and could statistically test the effects of treatment on biomass allocation and simultaneously correct the tree-size effect. After correction for the tree-size effect, the high irrigation or the high-fertigation associated DIF regimes altered biomass allocation to some extent. Additional N fertigation did not affect early stand growth but affected biomass allocation.