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The comparison of item response theory models for the Test of English as a Foreign Language (TOEFL) was extended to an equating context as simulation trials were used to "equate the test to itself." Equating sample data were generated from administration of identical item sets. Equatings that used procedures based on each model (simple item response, three-parameter logistic, and Rasch models) were accomplished under several conditions and the results were compared. Conditions varied by sample size, anchor test difficulty, and the TOEFL section equated. The largest discrepancies between scores identified as comparable occurred for the three-parameter logistic (3PL) and the modified Rasch models at the lower extreme scores, and for the simple models at the upper extreme score. If it is true that the cut scores for most institutions occur in the mid-score ranges, the findings suggest that the 3PL should not be used if equating samples are substantially reduced from the present size. The other models are promising for small sample equating, with the one-parameter logistic models being most promising. Six tables and six figures illustrate the analysis. (Contains 10 references.) (SLD)

Descriptors: Comparative Analysis, Cutting Scores, English (Second Language), Equated Scores, Item Response Theory, Research Methodology, Sample Size, Simulation, Statistical Analysis, Test Items

Author: Boldt, R. F.


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