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An Approach to Mental Test Theory

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord
Frederic M. Lord*
Affiliation:
Educational Testing Service
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Abstract

It currently seems to me that the heart of mental test theory is the concept of true score.

The trouble starts as soon as it is realized that the actual test score obtained by a particular individual might just as well have been some numerical value other than the one actually observed. The individual examinee might have guessed differently, might have been less nervous, or might have slept better the night before. The testing conditions might have been different–lighting, facilities for use of paper and pencil, presence or absence of distraction. Finally, any one of many different but equally appropriate psychological tests might have been constructed and administered.

Mental test theory must deal with all these kinds of disturbing influences. However, we are not really interested in each of the different test scores that an examinee might obtain under all sorts of conditions. We are interested in something approximated by these scores. This something may be called the true score on the test.

Type
Original Paper
Information
Psychometrika , Volume 24 , Issue 4 , December 1959 , pp. 283 - 302
Copyright
Copyright © 1959 The Psychometric Society

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Footnotes

*

Presidential address delivered to the Psychometric Society, Cincinnati, Ohio, September 8, 1959.

†

Much of the research discussed here was carried out under Contracts Nonr-2214 (00) and -2752(00) with the Office of Naval Research, Department of the Navy.

References

Barton, D. E. and Dennis, K. E. The conditions under which Gram-Charlier and Edgeworth curves are positive definite and unimodal. Biometrics, 1952, 39, 425–426.CrossRefGoogle Scholar
Basmann, R. L. The computation of generalized classical estimates of coefficients in a structural equation. Econometrica, 1959, 27, 72–81.CrossRefGoogle Scholar
Buckingham, R. A. Numerical methods, London: Pitman, 1957.Google Scholar
Collatz, L. Numerische Behandlung von Differential-Gleichungen, Berlin: Springer, 1951.Google Scholar
Crout, P. D. An application of polynomial approximation to the solution of integral equations arising in physical problems. J. math. Phys., 1940, 19, 34–92.CrossRefGoogle Scholar
Cureton, E. E. and Tukey, J. W. Smoothing frequency distributions, equating tests, and preparing norms. Amer. Psychologist, 1951, 6, 404–404.Google Scholar
Ferguson, T. On the existence of linear regression in linear structural relations. Univ. Calif. Publications in Statistics, 1955, 2, 7.Google Scholar
Gaffey, W. R. A consistent estimator of a component of a convolution. Ann. math. Statist., 1959, 30, 198–205.CrossRefGoogle Scholar
Geary, R. C. Inherent relations between random variables. Proc. Roy. Irish Acad., 1942, 47, 63–76.Google Scholar
Geary, R. C. Determination of linear relations between systematic parts of variables with errors of observation the variances of which are unknown. Econometrica, 1949, 17, 30–58.CrossRefGoogle Scholar
Geary, R. C. Relations between statistics: The general and the sampling problem when the samples are large. Proc. Roy. Irish Acad., 1943, 49, 177–196.Google Scholar
Johnson, N. L. and Rogers, C. A.. The moment problem for unimodal distributions. Ann. math. Statist., 1951, 22, 433–439.CrossRefGoogle Scholar
Kendall, M. G. The advanced theory of statistics, London: Griffin, 1948.Google Scholar
Kendall, M. G. Regression, linear structure, and functional relationship. Biometrika, 1951, 38, 11–25.CrossRefGoogle Scholar
Koopmans, T. C.and Reiersøl, O. The identification of structural characteristics. Ann. math. Statist., 1950, 21, 165–181.CrossRefGoogle Scholar
Lord, F. M. Statistical inferences about true scores. Psychometrika, 1959, 24, 1–17.CrossRefGoogle Scholar
Lord, F. M. Use of true-score theory to predict moments of univariate and bivariate observed-score distributions. Princeton: Educ. Test. Serv. Res. Bull. 59-6, 1959.CrossRefGoogle Scholar
Lord, F. M. An empirical study of the normality and independence of errors of measurement in test scores. Psychometrika, in press.Google Scholar
Lord, F. M. Inferences about true scores from parallel test forms. Educ. psychol. Measmt, 1959, 19, 331–336.CrossRefGoogle Scholar
Lord, F. M. The joint cumulants of true values and errors of measurement. Ann. math. Statist., in press.Google Scholar
Madansky, A. The fitting of straight lines when both variables are subject to error. J. Amer. statist. Ass., 1959, 54, 173–205.CrossRefGoogle Scholar
Mallows, C. L. Note on the moment-problem for unimodal distributions when one or both terminals are known. Biometrics, 1956, 43, 224–227.CrossRefGoogle Scholar
Moran, P. A. P. A significance test for an unidentifiable relation. J. Roy. statist. Soc. B, 1956, 18, 61–64.CrossRefGoogle Scholar
Neyman, J. and Scott, E. L. Consistent estimates based on partially consistent observations. Econometrica, 1948, 16, 1–32.CrossRefGoogle Scholar
Pollard, H. Distribution functions containing a Gaussian factor. Proc. Amer. math. Soc., 1953, 4, 578–582.CrossRefGoogle Scholar
Reiersøl, O. Identifiability of a linear relation between variables which are subject to error. Econometrica, 1950, 18, 375–389.CrossRefGoogle Scholar
Robbins, H. An empirical Bayes approach to statistics. In Neyman, J. (Eds.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Vol. 1. Berkeley: Univ. California Press, 1956, 157–163.Google Scholar
Royden, H. L. Bounds on a distribution function when its firstn moments are given. Ann. math. Statist., 1953, 24, 361–376.CrossRefGoogle Scholar
Standish, C. N-dimensional distributions containing a normal component. Ann. math. Statist., 1956, 27, 1161–1165.CrossRefGoogle Scholar
Steinhaus, H. The problem of estimation. Ann. math. Statist., 1957, 28, 633–648.CrossRefGoogle Scholar
Tricomi, F. G. Integral equations, New York: Interscience, 1957.Google Scholar
Trumpler, R. J. and Weaver, H. F. Statistical astronomy, Berkeley: Univ. California Press, 1953.CrossRefGoogle Scholar
Tukey, J. W. Components in regression. Biometrics, 1951, 7, 33–69.CrossRefGoogle ScholarPubMed
Wallace, D. L. Asymptotic approximations to distributions. Ann. math. Statist., 1958, 29, 635–654.CrossRefGoogle Scholar
Wolfowitz, J. Estimation of the components of stochastic structures. Proc. Nat. Acad. Sci., 1954, 40, 602–606.CrossRefGoogle ScholarPubMed
Williams, E. J. Significance tests for discriminant functions and linear functional relationships. Biometrics, 1955, 42, 360–381.CrossRefGoogle Scholar
Zelen, M. Bounds on a distribution function that are functions ofμ 0 toμ 4. J. Res. Nat. Bur. Standards, 1954, 53, No. 6, paper 2556.CrossRefGoogle Scholar