Análise de experimentos fatoriais de dois fatores com tratamentos adicionais

Experiments using factorial arrangement of treatments are rather common and useful in agricultural research. The main advantage is the possibility of testing many hypotheses, allowing broader conclusions over different factors, studied simultaneously. Factorial arrangements are used to compare levels of each factor (main effects), and also to verify if the differences among levels of a given factor are dependent on the levels of the other factors (interacions). In the analysis of data from factorial experiments, difficulty is increased when additional treatments are included. Inclusion of one or more additional treatments is a quite common practice, since such treatments are usually taken as reference or standard for evaluation and comparasion of the remaimng treatments, or aiming complementary information. This increase of difficulty is however low, compared to the advantages. As in literature there are few references about the statistical analysis of factorial experiments with additonal treatments, and given straightforward use in experimentation, the objective of this work was the presentation of approach for the use of factorial experiments with additonal treatments trough the analysis of some examples using the SAS® software, with the corresponding theoretical development, obtaining the system of normal equations, estimators of the parameters and variance of contrasts among two treatment means. It is suggested that additional treatments should be used with caution. The analysis of variance of such kind of experiment was presented using matrix notation.

Processo infeccioso de Pseudocercospora musae e severidade da Sigatoka Amarela da bananeira em função do silício, potássio e cálcio em solução nutritiva

Yellow Sigatoka leaf spot, caused by Pseudocercospora musae (Mycosphaerella musicola), is one of main threats to banana production around the world. However, information regarding the infection process of P. musae and the influence of mineral nutrition on the disease severity could help with cultural control strategies and increase the fruit yield. Therefore, this work aimed to characterize the infectious process of P. musae in banana leaves, to study the effect of silicon (Si) and the interaction between potassium (K) and calcium (Ca) on the Yellow Sigatoka leaf spot severity. In the first study, samples were inoculated on the abaxial leaf surface with P. musae and analyzed at 12, 24, 36, 48, 72, 96, 120, 144, and 168 hours after inoculation (HAI) as well as 36 and 50 days after inoculation (DAI). The conidia germinated between 24 and 36 HAI and penetrated through the stomata between 96 and 120 HAI, or usually from 144 HAI. P. musae colonized intercellularly the spongy parenchyma at 36 DAI and inter- and intracellularly the palisade parenchyma at 50 DAI. The sporulation occurred at 50 DAI on the adaxial leaf surfaces. In the second study, banana plants grown in nutrient solution with 0; 0.5; 1.0; 1.8 and 3.6 mmol L -1 of silicic acid (H 4SiO 4) were inoculated with conidial suspension. The disease severity was assessed and data were integrated in the area under the disease severity progress curve (AUDSPC). The lower AUDSPC was 49.27% for the concentration of 3.05 mmol L -1 of H 4SiO 4 compared to plants grown without Si addition. Regarding silicon accumulation, at 3.6 mmol L -1 H4SiO 4, leaf Si content was 23.53% higher compared to the control. In the third study, plants grown in nutrient solution with 5 K concentrations (1, 2, 4, 6, and, 8 mmol L -1 ) combined with 5 Ca concentrations (1, 3, 5, 7, and, 9 mmol L -1 ), forming 25 treatments, were inoculated with conidial suspension. The disease severity was assessed and the data were integrated in the AUDSPC. There was no interaction between concentrations of K and Ca for AUDSPC, although the AUDSPC increased with the increase of K concentrations from 1 to 6 mmol L -1 . The K increase led to a reduction in chlorophyll a and b contents and in the N, P, Mg, B, Cu, Zn, and, Mn nutrients as well as increased the total plant dry weight.