Anomaly, Paradox and Progress

"The aim of science is to maximize the scope of solved empirical problems, while minimizing the scope of anomalous and conceptual problems" (Laudan, 1977, p. 66).

When comparing different research traditions, such as the "test score" and "scaling" traditions, progress should be evaluated in terms of the adequacy of solutions offered for both empirical (data dominated) anomalies and conceptual (theory dominated) paradoxes in educational and psychological measurement. An important question in the study of progress is: How do scientists react to anomalies and paradoxes?

Kuhn (1970) defines an anomaly as a violation of the "paradigm-induced expectations that govern normal science" (pp. 52-53). Anomalies are detected through empirical analyses and have formed the basis for most discoveries in the natural sciences. For Kuhn, the discovery of anomalies provides the impetus for paradigm change within a field of study. Anomalies are empirical difficulties that reflect differences between the observed and theoretically expected data.

A paradox is a statement that seems to be contradictory or absurd, but may in fact be true. Both anomalies and paradoxes appear only within the framework of specific theories. Crossing item characteristic curves (ICCs) are viewed as paradoxical within the framework of Rasch measurement. If ICCs cross for two items, then the item difficulty order reverses above and below the crossing point. When ICCs cross, sample- invariant item calibration cannot be achieved. Crossing ICCs are not viewed as paradoxical within the framework of the two- or three-parameter IRT models.

How does scientific progress occur? According to positivists, such as Popper, theories are abandoned when anomalies occur. Post-positivist scholars (Kuhn, Lakatos, Laudan) question this. Laudan, Laudan and Donovan (1988) have proposed seven theses regarding how scientists react to anomalies:

When a theory encounters an anomaly or a paradox, then scientists (1) believe that this reflects adversely on their skills rather than on the inadequacies of the theory.
(2) leave the anomaly/paradox unresolved.
(3) refuse to change their assumptions.
(4) ignore the anomaly/paradox as long as the theory continues to anticipate novel phenomena successfully.
(5) believe that the anomaly/paradox becomes grounds for rejecting the theory only if it persistently resists solution.
(6) introduce hypotheses which are not testable in order to save the theory.
(7) believe that the anomaly/paradox becomes acute only if a rival theory explains it.

Evidence from the natural sciences reported by Laudan et al. suggests that when problems in a theory are encountered by scientists, these problems are not ignored, but the theory is not immediately abandoned. Typically, the scientists who use the theory seek a way of explaining and dealing with the problem that is not ad hoc. If they cannot address the problem, then the theory is likely to be abandoned; this is even more likely if an alternative theory is available that can explain the problem. Laudan et al. do not distinguish between anomalies and paradoxes, and scientists probably react in the same way to both.

What roles have anomalies and paradoxes played in progress in measurement theory? How have measurement practitioners and theorists reacted to conceptual problems? In the next two columns, I will explore the seven theses using, as two case studies, the "attenuation paradox" and the crossing of item characteristic curves.

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

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

Laudan, R., Laudan, L., & Donovan, A. 1988. Testing theories of scientific change. In A. Donovan, L. Laudan, & R. Laudan (Eds.), Scrutinizing science: Empirical studies of scientific change (pp. 3-44). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Anomaly, Paradox and Progress, G Engelhard Jr. … Rasch Measurement Transactions, 1992, 6:2 p. 212

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
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

To be emailed about new material on
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from welcomes your comments:

Your email address (if you want us to reply):


ForumRasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website,

Coming Rasch-related Events
Oct. 6 - Nov. 3, 2023, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Facets),
Oct. 12, 2023, Thursday 5 to 7 pm Colombian timeOn-line workshop: Deconstruyendo el concepto de validez y Discusiones sobre estimaciones de confiabilidad SICAPSI (J. Escobar, C.Pardo)
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),


The URL of this page is