ABSTRACT
In this chapter we introduce completely randomized designs for the situation where we have one treatment factor. These designs consist of a random allocation of the the experimental units to the different treatments (without taking into account any other structure or information). The corresponding model is known as the one-way analysis of variance (ANOVA) model. We show how the variation of the response can be partitioned into multiple sources which leads to the concept of an ANOVA table. It is used to construct the so-called F-test which can be understood as an extension of the two-sample t-test. In addition, we illustrate how the different parametrizations of the model can be used in R which is crucial for a correct understanding of the model coefficients. In order to check the model assumptions, we present suitable plots. Additional topics include nonparametric approaches, power analysis (which answers the question how many observations are needed for a study) and how additional covariates can be incorporated into the model.
