Three-Way and Higher-Order Nested Classifications

The results of the preceding chapter can be readily extended to the case of three-way and the general q-way nested or hierarchical classifications. As an example of a three-way nested classification, suppose a chemical company wishes to examine the strength of a certain liquid chemical. The chemical is made in large vats and then is barreled. To study the strength of the chemical, an analyst randomly selects three different vats of the product. Three barrels are selected at random from each vat and then three samples are taken from each barrel. Finally, two independent measurements are made on each sample. The physical layout can be depicted schematically as shown in Figure 7.1 In this experiment, barrels are nested within the levels of the factor vats and samples are nested within the levels of the factor barrels. This is the so-called three-way nested classification having two replicates or measurements. In this chapter, we consider the three-way nested classification and indicate its generalization to higher-order nested classifications.