Joe H. Ward

Abstract A procedure for forming hierarchical groups of mutually exclusive subsets, each of which has members that are maximally similar with respect to specified characteristics, is suggested for use in large-scale (n > 100) studies when a precise optimal solution for a specified number of groups is not practical. Given n sets, this procedure permits their reduction to n − 1 mutually exclusive sets by considering the union of all possible n(n − 1)/2 pairs and selecting a union having a maximal value for the functional relation, or objective function, that reflects the criterion chosen by the investigator. By repeating this process until only one group remains, the complete hierarchical structure and a quantitative estimate of the loss associated with each stage in the grouping can be obtained. A general flowchart helpful in computer programming and a numerical example are included.

Abstract A procedure for forming hierarchical groups of mutually exclusive subsets, each of which has members that are maximally similar with respect to specified characteristics, is suggested for use in large-scale (n > 100) studies when a precise optimal solution for a specified number of groups is not practical. Given n sets, this procedure permits their reduction to n − 1 mutually exclusive sets by considering the union of all possible n(n − 1)/2 pairs and selecting a union having a maximal value for the functional relation, or objective function, that reflects the criterion chosen by the investigator. By repeating this process until only one group remains, the complete hierarchical structure and a quantitative estimate of the loss associated with each stage in the grouping can be obtained. A general flowchart helpful in computer programming and a numerical example are included.

Abstract : This volume develops the application of multiple linear regression as a general approach to the formulation and analysis of research problems. The approach, while powerful, is direct and conceptually simple, less restrictive than multivariate correlation techniques, and suited to problems involving binary-coded information. Illustrative problems are largely from the behavioral sciences. Chapter headings are: Introduction to Vectors, Formulation of Problems (Categorical Predictors), Formulation of Problems (Continuous Predictors), Generation of New Vectors, Treatment Effects Obtained in Presence of Concomitant Variables, Other Applica tions of the General Regression Approach. (Author)