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A Strong True-Score Theory, With Applications

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Item Response Theory, Mathematical Models, Test Theory, True Scores


A "strong" mathematical model for the relation between observed scores and true scores is developed. This model can be used to estimate the frequency distribution of observed scores that will result when a given test is lengthened; to equate true scores on two tests by the equipercentile method; to estimate the frequencies in the scatterplot between two parallel (nonparallel) tests of the same psychological trait, using only the information in a (the) marginal distribution(s); to estimate the frequency distribution of a test for a group that has taken only a short form of the test (this is useful for obtaining norms); to estimate the effects of selecting individuals on a fallible measure; to effect matching of groups with respect to true score when only a fallible measure is available; to investigate whether two tests really measure the same psychological function when they have a nonlinear relationship; and to describe and evaluate the properties of a specific test considered as a measuring instrument. The model has been tested empirically, using it to estimate bivariate distributions from univariate distributions, with good results, as checked by chi-square tests.

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