Emprego do modelo superparametrizado em experiemento fatorial desbalanceado com dois fatores

Abstract

In agricultural research it is common to study simultaneously various factors and natural loss of observations frequently leads to unbalanced experiments. Thus it is necessary to know which hypothesis can be tested in the statistical systems. In a missing cells scenario the interpretation is even more complex. In general, the hypothesis on main effects of one of these factors contains the main effects of other factors and of effects of interactions. The aim of this work is to develop ANOVA schemes for the overparameterized model to unbalanced data and, or with situations with missing cells. Additionally we call attention to correct identification and interpretation of the hypothesis associated with the four types of sum of squares given by SAS-GLM procedure. Two distinct cases were analyzed, namely: using data referring to commercial weight of carrots, arising from a completely randomized experiment and, using a factorial design with two planting factors (cultivation and the phasis of the moon). We conclude that the estimable functions of a factor involves a linear combination of both main effects and interaction parameters for both Type III and Type IV Sum of Squares. The order of the main effects changes type I Sum of Squares. Thus, when there are missing cells in the two-factor model, the four types of sum of square for main effects are different and the order is fundamental to obtain the correct type I hypothesis. When missing cells happens, the identification of the estimable functions is more complex and the hypotheses are difficult to interpret. In the estimable functions for interaction, interaction parameters appears as expected. In this case, differences between levels of one main effect factor can only be estimated in the presence of average effects due to the other factor B and the interaction.