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The Axioms and Principal Results of Classical Test Theory

Novick, Melvin R.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Mathematical Models, Psychometrics, Test Theory


Following an approach due to Guttman the axioms of the classical test theory model are shown to be derivable as constructions from a specified sampling rule and from the assumption that the observed score of an arbitrarily specified or randomly selected person may be considered as an observation of a random variable having finite and positive variance. Without further assumption the reliability of a test is defined. Parallel measurements are then independently defined, and the concept of replication is explicated. The derived axioms of the classical test theory model are then stated in a refined form of Woodbury's stochastic process notation, and the basic results of this model are derived. The assumptions of experimental independence, homogeneity of error distribution, and conditional independence are related to the classical model and to each other. Finally, a brief sketch of some stronger models assuming the independence of error and true scores or the existence of higher-order moments of error distributions or those making specific distributional assumptions is given.

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