Progress in Measurement Theory

We must explain why science - our surest example of sound knowledge - progresses as it does, and we first must find out how, in fact, it does progress.
Thomas Kuhn, 1970a, p.20

The adequacy or effectiveness of individual theories is a function of how many significant empirical problems they solve, and how many important anomalies and conceptual problems they generate.
Larry Laudan, 1977, p.119

How should "progress" be defined and evaluated for measurement theory? Progress can be defined in different ways. Bury (1932) provides a historical analysis of how the idea of progress has changed over time. This change continues. For some philosophers of science, progress is defined in terms of the number of empirical problems successfully solved (Kuhn, 1970b). Empirical problems are substantive questions about objects which constitute the domain of any given science (Laudan, p.15).

Other philosophers argue that the overall problem-solving effectiveness of a theory is determined by assessing the number and importance of empirical problems which the theory solves and deducting therefrom the number and importance of the anomalies and conceptual problems which the theory generates (Laudan, p.68). Conceptual problems are characteristics of theories with no existence independent of the theories themselves. Conceptual problems depend on the well-foundedness of the conceptual structures (e.g., theories) which have been devised to answer the first-order [empirical] questions (Laudan, p.48). Since conceptual problems could devalue even the most effective solution to an empirical problem, surely our definition of progress must encompass both components.

What are the major empirical and conceptual measurement problems in the social sciences? Are some problems more important than others? What are the criteria for defining acceptable solutions to crucial problems? Can objective criteria be developed for comparing the problem-solving effectiveness of different measurement theories?

In item response theory, IRT, the responses of individuals to test items define the objects of study. Empirical questions can be raised such as "How well does the model fit the data?" or "How well do data fit the model?" If empirical criteria alone defined problem-solving effectiveness, then the better theory would provide the better model-data fit. When, however, conceptual problems are also considered, theory evaluations must include the illogical consequences of some measurement theories, such as the crossed item characteristic curves that follow from Birnbaum's model, and the attenuation paradox of "true score" theory.

Once the crucial empirical and conceptual problems are defined, progress can be examined by comparing the problem-solving effectiveness of competing theories. The effectiveness of a single measurement theory can also be examined over time by evaluating how well it deals with new problems that did not exist when it was formulated. Computerized adaptive testing (CAT) systems did not exist when Spearman laid the groundwork for "true score" theory, nor when Rasch developed his measurement theory. We now see that "true score" theory cannot provide a useful solution for CAT measurement problems. On the other hand, practical CAT systems have been developed using the Rasch model.

Professor George Engelhard, Jr.
Emory University
Division of Educational Studies

Bury J.B. 1932. The idea of progress: An inquiry into its growth and origin. New York: Dover.

Kuhn T. 1970a. Logic of discovery or psychology of research? In Lakatos and Musgrave, Criticism and the growth of knowledge. London: Cambridge University Press.

Kuhn T. 1970b. The structure of scientific revolutions. 2nd Edition, enlarged. Chicago: The University of Chicago Press.

Laudan L. 1977. Progress and its problems: Towards a theory of scientific growth. Berkeley, CA: University of California Press.

Progress in Measurement Theory. G. Engelhard, Jr. … Rasch Measurement Transactions, 1992, 6:1, 204

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Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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