ABSTRACT
This chapter introduces the concept of factorial treatment structure which arises if a treatment is a combination of two (or more) factors. A typical question is whether there is an interaction (interplay) between these factors. We therefore introduce the two-way ANOVA model which consists of main effects and interaction effects. We show how the model parameters can be estimated for a balanced design (with the same number of observations for all treatment combinations) and how statistical tests can be derived. A special case is the case where we only have a single observation per treatment combination. For unbalanced data, multiple approaches using different types of sum of squares are introduced. As an outlook we consider the case of more than two factors and shortly discuss the issues of nonparametric approaches.
