Latent Structure Analysis of the TOEFL® Test

Author(s):
Boldt, Robert F.
Publication Year:
1988
Report Number:
RR-88-27, TOEFL-RR-28
Source:
Language Testing, 1989, 6(2), 123-142.
Document Type:
Subject/Key Words:
English as a second language factor structure item response theory language tests structural analysis

Abstract

The results of equating studies are supportive of the use of IRT methods for TOEFL® equating, but there remains a discrepancy between the assumptions of the equating and the diversity of the population served. The IRT model assumes that, except for chance effects, the performance of individuals is entirely accounted for by their status on a single latent proficiency variable. But the TOEFL candidate population appears to be sufficiently diverse that different groups might exist, each with its own latent variable. Informal studies indicate that such is the case. The purpose of the study reported here was to identify such groups, if any, and to explore the implications of the results. The basic and very surprising outcome of this study was the finding that a single factor accounted for virtually all the proportions of joint item successes. This result was obtained for all three TOEFL sections. Also for each section, proportions of joint item success were proportional to the products of the item difficulties. Both of these results indicate that latent group effects are small. The results of the present study are consistent with the use of section equating using item response theory and with the use of the restrictive assumption of proportionality of item response curves; the probability of correct response is a product of two components, a function of ability and an item constant. This is a single parameter model that could serve as a basis for item calibration and equating. The model would lead to simplified procedures. The result also suggests that, when assembling operational tests, using those items for which the proportion of joint successes is most nearly proportional to their difficulties would reduce latent group effects.

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