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Estimation of true score and error variance for tests under various equivalence assumptions

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Abstract

Maximum-likelihood estimators of true score variance and error variance for mental tests are derived for six different models of equivalent measurements. Statistical properties of the estimators are examined. Main emphasis is placed upon essentiallyτ-equivalent measurements. A statistical criterion for this type of measurement is given. The solution of the comparatively simple maximum-likelihood equations is effected by means of a rapid Newton-Raphson procedure. Two different initial estimators are considered and their relative merits in terms of second moments evaluated. Four numerical examples are appended by way of illustration.

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References

  • Anderson, T. W.Introduction to multivariate statistical analysis. New York: Wiley, 1958.

    Google Scholar 

  • Gulliksen, H.Theory of mental tests. New York: Wiley, 1950.

    Google Scholar 

  • Jöreskog, K. G. Statistical models for congeneric test scores.Proceedings, 76th Annual Convention, APA, 1968, 213–214.

  • Kristof, W. Statistical inferences about the error variance.Psychometrika, 1963,28, 129–143. (a)

    Google Scholar 

  • Kristof, W. The statistical theory of stepped-up reliability coefficients when a test has been divided into several equivalent parts.Psychometrika, 1963,28, 221–238. (b)

    Google Scholar 

  • Lord, F. M., & Novick, M. R.Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley, 1968.

    Google Scholar 

  • Novick, M. R., & Lewis, C. Coefficient alpha and the reliability of composite measurements.Psychometrika, 1967,32, 1–13.

    Google Scholar 

  • Wilks, S. S. Sample criteria for testing equality of means, equality of variances, and equality of covariances in a normal multivariate distribution.Annals of Mathematical Statistics, 1946,17, 257–281.

    Google Scholar 

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Authors and Affiliations

  1. Educational Testing Service, USA

    Walter Kristof

Authors
  1. Walter Kristof
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Additional information

Paper read at the Mathematical Psychology Meeting, August 28, 1968, at Stanford, Calfornia.

This research was supported in part by the National Institute of Child Health and Human Development, Research Grant 1 P01 HD01762.

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Kristof, W. Estimation of true score and error variance for tests under various equivalence assumptions. Psychometrika 34, 489–507 (1969). https://doi.org/10.1007/BF02290603

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  • DOI: https://doi.org/10.1007/BF02290603

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