Formula Scoring, Basic Theory and Applications

Abstract

Formula scoring is a systematic study of measurement statistics expressed as sums of products of item scores. The theory is currently being used to compute non-parametric estimates of ability distributions, item response functions, and option response functions. The theory has been used to design algorithms for estimating item response functions from adaptive test data (on-line calibration), monitoring and correcting drift in observed score distributions for adaptive tests (on-line equating), computing optimal tests for cheating, and combining appropriateness measurement information from several subtests. In this paper a portion of the theory is developed from a few principles. Applications are considered to the problems of deciding whether ability has the same distribution in two demographic groups, to finding latent class models that are equivalent to item response models, and to controlling drift in adaptive testing programs. Keywords: Latent trait theory, Item response theory, Formula score, Rasch model, Equating, Foundations, Quasidensities, Densities, Non-parametric density estimation, Ability distributions, Identifiability.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1989
Accession Number
ADA218368

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  • Michael V. Levine

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  • University of Illinois Urbana–Champaign

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