Partially Nested Classifications

In the preceding chapters, we discussed classification models involving several factors that are either all crossed or all nested. Occasionally, in a multifactor experiment, some factors will be crossed and others nested. Such designs are called partially nested (hierarchical), crossed-nested, nested-factorial, or mixed-classification designs. For example, suppose that in a study involving an industrial experiment it is desired to test three different methods of a production process. For each method, five operators are employed. The experiment is carried out over a period of four days and three observations are obtained for each combination of method, operator, and day. Because of the nature of the experiment, the five operators employed under Method I are really individuals different from the five operators under Method II or Method III and the five operators under Method II are different from those under Method III. The physical layout of such an experiment can be depicted schematically as shown in Figure 8.1 In this experiment, the days are crossed with the methods and operators, and operators are nested within methods.