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-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
Rasch Books and Publications: Winsteps and Facets
Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
Facets Tutorials - free
Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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
May 17 - June 21, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps),
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden
June 21 - July 19, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Winsteps),
Aug. 5 - Aug. 6, 2024, Fri.-Fri. 2024 Inaugural Conference of the Society for the Study of Measurement (Berkeley, CA), Call for Proposals
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),
Oct. 4 - Nov. 8, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps),
Jan. 17 - Feb. 21, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps),
May 16 - June 20, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps),
June 20 - July 18, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets),
Oct. 3 - Nov. 7, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps),


The URL of this page is