SEVERAL of the terms of the above title are analogous to key concepts in factor analysis; types correspond to factors, and typal relevancies correspond to factor loadings. These terms have similar meanings to the corresponding ones in Thurstonian factor analysis except for one fundamental difference ; the terms of elementary linkage analysis are here applied to a theory of psychological structure which is basically different from simple structure as developed by Thurstone (16, p. 181). However, data are sometimes so interrelated that the difference in theory does not express itself in empirical results; linkage analysis sometimes yields results very similar to, or even identical with, those of rotated factor-analytic solutions.Advantages of elementary linkage analysis are its provision for investigating a particular theoretical position, its speed, and its objectivity. A fifteen variable matrix can be analyzed into objectively determined types in five to ten minutes, all operations with only pencil and paper. The original solution of a linkage analysis gives the desired structure; no rotation is required.
Need for the MethodElementary linkage analysis is a method of clustering. It can be used to cluster either people or items, or any objects, for that matter, which have distinctive cluster-characteristics.In order to make our discussion somewhat concrete, rather than abstract, we shall talk of cluster methods as procedures 1 This article was completed while the author was on the Faculty of the University of Illinois.
EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 1967, 27, 21-46. ScmrrCE often advances by a theory concerning some aspects of reality. The theory grows out of observation and thought. The observation may be either relatively crude or highly controlled, depending usually on the sophistication of the subject matter involved. The observation may be made by the theoretician himself or by study of observations pursued and reported by others.Hypotheses are developed as logical deductions from the theory. If the theory is correct, then the hypotheses must also be correct. A more desirable relationship is one in which the theory is correct if the hypothesis is correct. Few if any hypotheses hold this relationship to a theory in any absolute sense.The dependability of the relationship between hypotheses and theory is usually a matter of degree. In most instances, a set of hypotheses is more dependable than a single hypothesis, and n carefully developed hypotheses are usually more dependable than any subset of them.Hypotheses have a scientific value which theories do not usually possess: their validity can be directly tested empirically.Science builds theory by testing hypotheses. Hypotheses are used to help generate research designs which test the hypotheses. If a hypothesis is investigated and substantiated, it gives support to a theory and the investigator develops other, hopefully more crucial, hypotheses which can in turn be tested. If, on the other hand, a hypothesis is not substantiated, the investigator usually revises his theory and develops new hypotheses for testing.
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