Fractional factorials in a case study nutrition experiment with banana trees

Abstract

In this paper we study combining designs concatenating levels from a full factorial for some factors with screening alternatives for the others. This was done to deal with a practical situation in plant nutrition experiments. The original problem was a study design for 14 potential factors in banana tree nutrition, and researchers imagined four full factorials were needed to test their hypothesis, being two from the 33 and two of the 34 series. As this would demand at least 216 experimental units and facing limited resources we seek for a different planning strategy. The idea was to combine in the same experiment four instances of DSD (Denitive Screening Designs) for 10 three-level factors, each in a different block, with a fraction of the full factorial of the 34 series. A central point treatment, with average level for all factors, was present in all blocks. Interchange algorithms were used to concatenate the factor levels. Resulting optimized design was compared to the designs sampled following the same principle. Design comparison criterion was the expected average variance of the estimates for factors (Ar optimality). Optimization reduced 4.02% of the average values of the criterion in a reference population of sampled designs. It was possible to show that the variance for linear and quadratic effects in the full factorial were higher than in the optimized plan. As an example, the analysis of an actual eld trial is presented. Authors recommend the use of fractional factorial strategy including DSD designs in agronomic trials, specially in the screening phase.