@article{RIBEIRO_CAMPOS_PIO_BUENO FILHO_2019, title={FRACTIONAL FACTORIALS IN A CASE STUDY NUTRITION EXPERIMENT WITH BANANA TREES}, volume={37}, url={http://www.biometria.ufla.br/index.php/BBJ/article/view/402}, DOI={10.28951/rbb.v37i3.402}, abstractNote={<p>In this paper we study combining designs concatenating levels from a full&nbsp;factorial for some factors with screening alternatives for the others. This was done to&nbsp;deal with a practical situation in plant nutrition experiments. The original problem&nbsp;was a study design for 14 potential factors in banana tree nutrition, and researchers&nbsp;imagined four full factorials were needed to test their hypothesis, being two from the&nbsp;3<sup>3</sup> and two of the 3<sup>4</sup> series. As this would demand at least 216 experimental units&nbsp;and facing limited resources we seek for a different planning strategy. The idea was to&nbsp;combine in the same experiment four&nbsp; instances of DSD (Denitive Screening Designs)&nbsp;for 10 three-level factors, each in a different block, with a fraction of the full factorial of&nbsp;the 3<sup>4</sup> series. A central point treatment, with average level for all factors, was present in&nbsp;all blocks. Interchange algorithms were used to concatenate the factor levels. Resulting&nbsp;optimized design was compared to the designs sampled following the same principle.&nbsp;Design comparison criterion was the expected average variance of the estimates for&nbsp;factors (A<sub>r</sub> optimality). Optimization&nbsp; reduced 4.02% of the average values of the&nbsp;criterion in a reference population of sampled designs. It was possible to show that&nbsp;the variance for linear and quadratic effects in the full factorial were higher than in the&nbsp;optimized plan. As an example, the analysis of an actual eld trial is presented. Authors&nbsp;recommend the use of fractional factorial strategy including DSD designs in agronomic&nbsp;trials, specially in the screening phase.</p>}, number={3}, journal={Brazilian Journal of Biometrics}, author={RIBEIRO, Paulo César Moraes and CAMPOS, Matheus Pena and PIO, Leila Aparecida Salles and BUENO FILHO, Júlio Sílvio de Sousa}, year={2019}, month={Sep.}, pages={335–349} }