Nested Models

In some situations, the levels of one factor are not the same in each of the levels of the other factor, that is, it is not possible to determine all the possible treatment combinations that appear when the factors are crossed. Nested designs are an important experimental design in science, and they have some advantages over the 2-way ANOVA design, but they also have limitations. The nested model that we are discussing in this section is a two factor ANOVA, but it is incomplete compared to the fully crossed 2-way design. We cannot perform the typical two-factor ANOVA because we cannot get a mean of the different levels of factor 1 by combining the same levels of the factor 2; the data is not crossed. Instead, each level of nested factor is paired with one and only one level of the other factor.