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 Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	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
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	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	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
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
Other 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

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