Fatoriais fracionários em um exemplo de triagem de fatores na nutrição de bananeiras

Abstract

This thesis is derived from a case study in plant nutrition where the researchers’ demand was to plan an experiment involving 14 factors representing supplements for banana fertilization, being seven soil fertilizers and seven leaf fertilizers. The objective was to evaluate the changes in growth, physiology and productivity, provided by these factors. The initial size the researchers envisioned for the experiment was 216 experimental units. This was an important constraint for researchers because of the availability of only 90 experimental units. The solution (experimental design) proposed for the experiment was based on the design of screening designs. The idea was to combine replicates of this design in each block in a complete factorial, in the same experiment. Exchange and Interchange algorithms were employed to concatenate the four factor levels of a complete factorial (3 4 series) with 10 a factorial fractional factors, consisting of series screening designs (3 10 6 ) in four blocks that additionally contain the 0 level for all factors. The objective of maintaining the fractional factorial was to verify the efficiency of separate analyzes of each block of the complete factorial, for didactic purposes, for the researchers’ interest. The model considered the effects of local control, pure main and quadratic effects of all factors, besides the effects of double factorial interactions of the complete factorial. The efficiency criterion for the choice of experimental points was the expected mean variance of the estimates of the effects of all factors, without considering the effects of blocks (A-Criterion - restricted optimality). After one round of interchanges the variance of the best design was diminished 4; 02% the average variance over possible designs distribution. With the best design found it was possible to estimate all the effects of interest. Additionally the actual experiment was evaluated at six months for some agronomic traits. The plan underwent some changes in the implementation and the loss of efficiency due to this problem was calculated by calculating the optimality criterion for the actual design. This design was changed in practice and was suboptimal, however it was relatively efficient, leading to assertions of significance by the F test for several of the factors in a preliminary study . It was also possible to show that the variance of the factorial-derived effects estimates was greater than the estimates of principal effects and quadratic terms in the fractional factorial. In this way, it is recommended the greater use in agronomy, of fractional factorials, or of combined designs that involve complete factorial and fractional factorial, since they are a flexible strategy and of greater precision in experimentation.