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Abstract

Two concepts of “true score” in test theory are examined. Under one concept, the true score is identified with the expected value of the observed score, and it follows that reliability is the ratio of true variance to observed variance. Under the other concept, the true score is a constant which is not necessarily equal to the expected value of the observed score, and it follows that reliability is not necessarily equal to the ratio of true variance to observed variance. Axioms are presented which encompass both points of view, and explicit formulas relating the two kinds of true scores are derived by representing all scores and components of scores as random variables with the same associated probability space.

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References

Burke

C. J.

Measurement scales and statistical models. In Marx

M. H.

(Ed.), Theories in contemporary psychology. New York: Macmillan, 1963. Pp. 147–159.

Burrill

C. W.

Measure, integration, and probability. New York: McGraw-Hill, 1972.

Feller

An introduction to probability theory and its applications. Vol. II. New York: Wiley, 1966.

Frary

R. B.

Elimination of the guessing component of multiple-choice test scores: Effect on reliability and validity. Educational and Psychological Measurement, 1969, 29, 665–680. (a)

Frary

R. B.

Reliability of multiple-choice test scores is not the proportion of variance which is true variance. Educational and Psychological Measurement, 1969, 29, 359–365. (b)

Guttman

A basis for analyzing test-retest reliability. Psychometrika, 1945, 10, 255–282.

Guttman

Reliability formulas that do not assume experimental independence. Psychometrika, 1953, 18, 123–130.

Guttman

Review of F. M. Lord & M. R. Novick, Statistical theories of mental lest scores. Psychometrika, 1969, 34, 398–404.

Horst

Psychological measurement and prediction. Belmont, Calif.: Wadsworth, 1966.

10.

Loève

Probability theory. Princeton, N. J.: Van Nostrand, 1963.

11.

Loevinger

Objective tests as instruments of psychological theory. Psychological Reports, 1957, 3, 635–694.

12.

Lord

F. M.

Novick

M. R.

Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley, 1968.

13.

Novick

M. R.

The axioms and principal results of classical test theory. Journal of Mathematical Psychology, 1966, 3, 1–18.

14.

Thorndike

R. L.

Reliability. In Proceedings of the 1963 Invitational Conference on Testing Problems. Princeton, N. J.: Educational Testing Service, 1964. Pp. 23–32.

15.

Zimmerman

D. W.

Williams

R. H.

Chance success due to guessing and non-independence of true scores and error scores in multiple-choice tests: Computer trials with prepared distributions. Psychological Reports, 1965, 17, 159–165.

Two Concepts of “True Score” in Test Theory

Abstract

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References