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Sampling fluctuations resulting from the sampling of test items

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Abstract

Sampling fluctuations resulting from the sampling of test items rather than of examinees are discussed. It is shown that the Kuder-Richardson reliability coefficients actually are measures of this type of sampling fluctuation. Formulas for certain standard errors are derived; in particular, a simple formula is given for the standard error of measurement of an individual examinee's score. A common misapplication of the Wilks-Votaw criterion for parallel tests is pointed out. It is shown that the Kuder-Richardson formula-21 reliability coefficient should be used instead of the formula-20 coefficient in certain common practical situations.

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References

  1. Cramér, H. Mathematical methods of statistics. Princeton Univ. Press, 1946.

  2. Cronbach, L. J. Coefficient alpha and the internal structure of tests.Psychometrika, 1951,16, 297–334.

    Google Scholar 

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

    Google Scholar 

  4. Hooke, R. Sampling from a matrix, with applications to the theory of testing. Statistical Research Group, Princeton University. Memorandum Report 53, 1953. (Dittoed.)

  5. Kendall, M. G. The advanced theory of statistics. London: Charles Griffin and Co., 1948. 2 vols.

    Google Scholar 

  6. Kuder, G. F. and Richardson, M. W. The theory of the estimation of test reliability.Psychometrika, 1937,2, 151–160.

    Google Scholar 

  7. Mood, A. M. Introduction to the theory of statistics. New York: McGraw-Hill, 1950.

    Google Scholar 

  8. Peters, C. C. and Van Voorhis, W. R. Statistical procedures and their mathematical bases. New York: McGraw-Hill, 1940.

    Google Scholar 

  9. Tucker, L. R. A note on the estimation of test reliability by the Kuder-Richardson formula (20).Psychometrika, 1949,14, 117–119.

    Google Scholar 

  10. Votaw, D. F., Jr. Testing compound symmetry in a normal multivariate distribution.Ann. math. Stat., 1948,19, 447–473.

    Google Scholar 

  11. Wilks, S. S. Sample criteria for testing equality of means, equality of variances, and equality of covariances in a normal multivariate distribution.Ann. math. Stat., 1946,17, 257–281.

    Google Scholar 

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Authors and Affiliations

  1. Educational Testing Service, USA

    Frederic M. Lord

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  1. Frederic M. Lord
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Most of the work reported here was carried out under contract with the Office of Naval Research. The writer is indebted to Professor S. S. Wilks, who has checked over certain critical portions of a draft of this paper.

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Lord, F.M. Sampling fluctuations resulting from the sampling of test items. Psychometrika 20, 1–22 (1955). https://doi.org/10.1007/BF02288956

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  • DOI: https://doi.org/10.1007/BF02288956

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