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An interval estimate for making statistical inferences about true scores

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Abstract

A numerical procedure is outlined for obtaining an interval estimate of the regression of true score on observed score. Only the frequency distribution of observed scores is needed for this. The procedure assumes that the conditional distribution of observed scores for fixed true score is binomial. The procedure is applied to several sets of test data.

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References

  • Copas, J. B. Compound decisions and empirical Bayes.Journal of the Royal Statistical Society, Series B, 1969,31, 397–425.

    Google Scholar 

  • Fiacco, A. V. and McCormick, G. P.Nonlinear programming: Sequential unconstrained minimization techniques. New York: Wiley, 1968.

    Google Scholar 

  • Fletcher, R. and Powell, M. J. D. A rapidly convergent descent method for minimization.Computer Journal, 1963,2, 163–168.

    Google Scholar 

  • Griffin, B. S. and Krutchkoff, G. Optimal linear estimators: An empirical Bayes version with application to the binomial distribution.Biometrika, 1971,58, 195–201.

    Google Scholar 

  • Jöreskog, K. G. Some contributions to maximum likelihood factor analysis.Psychometrika, 1967,32, 443–482.

    Google Scholar 

  • Karlin, S. and Shapley, L. S. Geometry of moment space.Memoirs of the American Mathematical Society, 1953,12.

  • Lord, F. M. A strong true-score theory, with applications.Psychometrika, 1965,30, 239–270.

    Google Scholar 

  • Lord, F. M. Estimating true-score distributions in psychological testing (an empirical Bayes estimation problem).Psychometrika, 1969,34, 259–299.

    Google Scholar 

  • Lord, F. M. and Cressie, N. An empirical Bayes procedure for finding an interval estimate.Sankhyā, in press.

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

    Google Scholar 

  • Maritz, J. S. Smooth empirical Bayes estimation for one-parameter discrete distributions.Biometrika, 1966,53, 417–429.

    Google Scholar 

  • Possé, C.Sur quelques applications des fractions continues algébriques. St. Petersbourg, Russie: L'Académie Impériale des Sciences, 1886.

    Google Scholar 

  • Robbins, H. An empirical Bayes approach to statistics. In J. Neyman (Ed.),Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 1956, 157–164.

    Google Scholar 

Download references

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This research was sponsored in part by the Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research, under Contract No. N00014-69-C-0017, Contract Authority Identification Number, NR No. 150-303, and Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.

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Lord, F.M., Stocking, M.L. An interval estimate for making statistical inferences about true scores. Psychometrika 41, 79–87 (1976). https://doi.org/10.1007/BF02291699

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  • DOI: https://doi.org/10.1007/BF02291699

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