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.