Emprego do modelo superparametrizado em experimento fatorial desbalanceado com dois e três fatores

Abstract

In agricultural research it is common to study various factors and this frequently leads to loss of observations, therefore forming an unbalanced experiment. This is a well-known problem for many years and in spite ofthere being developed various tavorite lost work techniques, not one is universally accepted as the only one. It is necessary to know the tested hypothesis behind the statistical systems and when there are missing cells the interpretation is even more complex, but generally, the hypothesis on principal effects ofone ofthese factors contains the principal effects of other factors and of effects of interactions. Another detail which influences the formulation ofhypothesis by involving parameters without interest, when there is a loss of cells and, by adopting an overparametrized model, this work meets the objective, developing the schemes of variance analysis ofunbalanced data and/or with missing cells, identify and interpret the hypothesis associated with square sums behind the procedure General Linear Models (GLM) ofStatistical Analysis System (SAS), which prove four types of square sums. Three distinct cases were analysed, using data reterring to commercial weight ofcarrots, arising from an experiment completely at random, using as factors cultivation and the moon's phases on planting, the model study as two factors and even the month ofplanting factor in the case ofthree factor models. With the obtained results, you can conclude when 1he data. is unbalanced, the estimated functions ofa factor involving the relative parameters ofthe factor and it's components ofinteraction where the factor is present; the square sum ofType I and II are equivalent; as are Type HFs equivalent as Type IV's and the order ofthe principie factors do not efrect the hypothesis ofType I. However when there are missing cells inthetwo-factor model, the four types ofsquare sums for the principal factor input are different and the order is fundamental to obtain the hypothesis ofType I. When loss of parts happens, the identification ofthe estimate functions is more complex and the hypotheses are difficult to interpret. In the estimable functions ofinteractions present parameters of the interaction itself