Complex analyses of variance: General problems

Problems in applying the analysis of variance are discussed. Emphasis is placed on using the technique to understand the data. The scale of the dependent variable is important for the analysis. Crossed and nested categories must be recognized. The error terms in the analysis depend on whether the classes of each independent variable are (1) all out of a few or (2) a few out of many. To simplify the analysis, mean squares should be aggregated with their error term when they are less than twice its size. An illustrative example is discussed in detail.Prepared in connection with research sponsored in part by the Office of Naval Research, in part by the Educational Testing Service, and in part by Lincoln Laboratory, a center for research operated by Massachusetts Institute of Technology with the joint support of the U. S. Army, Navy, and Air Force.