Thurstone Case 5, Rasch, DTF and DIF

Thurstone, 1931, Fig. 20. Seriousness of delinquencies.

Differential Test Functioning (DTF) and Differential Item Functioning (DIF) were investigated by Louis L. Thurstone using Case 5 of his "Law of Comparative Judgment" which is based on "discriminal differences" (Psychological Review, 1927, 34, 273-286).

240 children in Mendota, Illinois, were each asked to compare pairs of 13 delinquent activities and indicate which should be punished more severely. About a week later, they were shown a movie about the life of a gambler and then instructed to do their comparisons again. The results are shown here from "Influence of motion pictures on children's attitudes" (Journal of Social Psychology, 1931, 2, 291-305).

Thurstone's sample exhibited DTF. The spread of scale values on the second occasion was .95 of the first. This was attributed to increased boredom or indifference on the second occasion. Accordingly, in the Figure, Thurstone inflated the scale values for the second occasion by 1.05. "Gambler" exhibits noticeable DIF. The movie about the gambling lifestyle affected attitudes, at least that day.

Thurstone published the data for his analysis. This was reanalyzed with a Bradley-Terry (Rasch) model using Facets. The plot below (with 1 logit = 0.54 Thurstone units) shows the collinearity of scale values. The placement of the black triangles above the dotted trend line indicates the slight non-linearity of Thurstone "Before" relative to Rasch "Before" values. The "After" values are not adjusted for DTF so their narrower range is evident. Thurstone and Rasch coincide in their placement of "Gambler" in the "After" analyses. Rasch standard errors are about .05 units, so a DIF study shows the shift in "Gambler" to be highly significant. "Gangster" and "Beggar" show noticeable misfit "Before". None misfit "After".

John M. Linacre



Thurstone Case 5, Rasch, DTF and DIF. Thurstone LL, Linacre JM. … 16:3 p.892


Thurstone Case 5, Rasch, DTF and DIF. Thurstone LL, Linacre JM. … Rasch Measurement Transactions, 2002, 16:3 p.892



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

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