Two-Way Nested (Hierarchical) Classification

Abstract

In Chapters 3 through 5 we considered analysis of variance for experiments commonly referred to as crossed classifications. In a crossed-classification, data cells are formed by combining of each level of one factor with each level of every other factor. We now consider experiments involving two factors such that the levels of one factor occur only within the levels of another factor. Here, the levels of a given factor are all different across the levels of the other factor. More specifically, given two factors A and B, the levels of B are said to be nested within the levels of A, or more briefly B is nested within A, if every level of B appears with only a single level of A in the observations. This means that if the factor A has a levels, then the levels of B fall into a sets of b ₁, b ₂,…,b _a levels, respectively, such that the i-th set appears with the i-th level of A. These designs are commonly known as nested or hierarchical designs where the levels of factor B are nested within the levels of factor A.