A Note on the Analysis of Designed Experiments with Complex Treatment Structure

Many experiments involve a complex treatment structure, and it is not always immediately obvious how such experiments should be analysed. This paper shows by way of three examples how a suitable linear model can be formulated that provides a meaningful analysis of variance table and allows mean comparisons of interest to be obtained in a straightforward manner. Possible advantages of this approach compared to the use of linear contrasts are discussed. It is concluded that a well-chosen model can often considerably simplify the analysis and lead to useful statistical inferences. The approach advocated in this paper is going to be strongest when there is good design structure present.