Three-Way and Higher-Order Crossed Classifications

Abstract

Many experiments and surveys involve three or more factors. Multifactor layouts entail data collection under conditions determined by several factors simultaneously. Such layouts usually provide more information and often can be even more economical than separate one-way or two-way designs. The models and analysis of variance for the case of three or more factors are straightforward extensions of the two-way crossed model. The methods of analysis of variance for the two-way crossed classification discussed in the preceding two chapters can thus be readily generalized to three-way and higher-order classifications. In this chapter, we study the three-way crossed classification in some detail because it serves as an illustration as to how the analysis can be extended when four or more factors are involved. Generalizations to four-way and higher-order classifications are briefly outlined.