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The ‘Ability’ Scale in Item Characteristic Curve Theory

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord
Frederic M. Lord*
Affiliation:
Educational Testing Service, Princeton, New Jersey
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Abstract

For the six available sets of empirical data, the discrimination (slope) parameter of the logistic item characteristic curve was found to have a significant positive correlation over items with the difficulty (location) parameter. This unpleasant situation can be eliminated by a suitably chosen transformation of the ability scale. An example of the transformation is given and some empirical results of using the transformed scale are shown.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 2 , June 1975 , pp. 205 - 217
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

*

Research reported in this paper has been supported by grant GB-41999 from the National Science Foundation.

References

Birnbaum, A.. Some latent trait models and their use in inferring an examinee’s ability. In Lord, F. M., Novick, M. R. (Eds.), Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Hambleton, R. K. and Rovinelli, R.. A FORTRAN IV program for generating examinee response data from logistic test models. Behavioral Science, 1973, 18, 74–74.Google Scholar
Learmonth, G. P. and Lewis, P. A. W.. Naval Postgraduate School random number generator package LLRANDOM, 1973, Monterey, Calif.: Naval Post Graduate School.Google Scholar
Wingersky, M. S. and Lord, F. M.. A computer program for estimating examinee ability and item characteristic curve parameters when there are omitted responses, 1973, Princeton, N. J.: Educational Testing Service.Google Scholar