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

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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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