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A Theory of Test Scores and Their Relation to the Trait Measured

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


A number of important problems are generated by the fact that the peculiarities of the items in a test may sharply affect the shape of the frequency distribution and other properties of the test scores that we use as measures of the mental characteristics of a group of examinees. The present paper has developed a theory that, granted certain assumptions and restrictions, expresses the various properties and characteristics of test scores, in relation to each other and in relation to the underlying trait measured, as functions of the difficulties and intercorrelations of the items of which the test is composed. The formulations and conclusions reached will be valid for any set of test data that is compatible with the assumptions and restrictions made. The theory developed facilitates and clarifies the interpretation to be placed on test scores as measures of a mental trait; it makes it possible to predict the properties of the test scores that will be obtained when a specified test is administered to a specified group of examinees; it indicates how items should be selected in order to construct tests that will have optimum properties for specific purposes.

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