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On accuracy in reliability estimation

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Abstract

This study in parametric test theory deals with the statistics of reliability estimation when scores on two parts of a test follow a binormal distribution with equal (Case 1) or unequal (Case 2) expectations. In each case biased maximum-likelihood estimators of reliability are obtained and converted into unbiased estimators. Sampling distributions are derived. Second moments are obtained and utilized in calculating mean square errors of estimation as a measure of accuracy. A rank order of four estimators is established. There is a uniformly best estimator. Tables of absolute and relative accuracies are provided for various reliability parameters and sample sizes.

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References

  • Aroian, L. A. A certain type of integral.American Mathematical Monthly, 1953,50, 382–383.

    Google Scholar 

  • Cacoullos, T. A relation betweent andF-distributions.Journal of the American Statistical Association, 1965,60, 528–531.

    Google Scholar 

  • Feldt, L. S. The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty.Psychometrika, 1965,30, 357–370.

    Google Scholar 

  • Kendall, M. G. & Stuart, A.The advanced theory of statistics. Vol. 1, 2. New York: Hafner, 1958, 1961.

    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.

    Google Scholar 

  • Kristof, W. On the sampling theory of reliability estimation.Journal of Mathematical Psychology, 1970,7, 371–377.

    Google Scholar 

  • Kristof, W. On a statistic arising in testing correlation.Psychometrika, 1972,37, 377–384.

    Google Scholar 

  • Olkin, I. & Pratt, J. W. Unbiased estimation of certain correlation coefficients.The Annals of Mathematical Statistics, 1958,29, 201–211.

    Google Scholar 

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Authors and Affiliations

  1. Educational Testing Service, USA

    Walter Kristof

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  1. Walter Kristof
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Kristof, W. On accuracy in reliability estimation. Psychometrika 39, 23–29 (1974). https://doi.org/10.1007/BF02291574

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  • DOI: https://doi.org/10.1007/BF02291574

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