Skip to main content
SpringerLink
Log in

Constructing measures with maximum reliability

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

The scoring of response vectors to give maximum test-retest correlation is investigated. Simple sufficiency arguments show that the form of the best scores is very restricted. A general method is given for finding the best scores, deriving the best scores for the normal factor model, and showing by calculation of several particular cases that for a standard model for binary response it is easy to approximate the best scores.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bartholomew, D. J. (1984). Scaling binary data using a factor model.Journal of The Royal Statistical Society, Series B,46, 120–123.

    Google Scholar 

  • Bartholomew, D. J. (1987).Latent variable models and factor analysis. London: Charles Griffin & Company.

    Google Scholar 

  • Bartholomew, D. J., & Schuessler, K. F. (1991). Reliability of attitude scores based on a latent trait model. In P. Marsden (Ed.),Sociological methodology (pp. 97–123). Oxford: Blackwell.

    Google Scholar 

  • Bentler, P. M. (1968). Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis.Psychometrika, 33, 335–345.

    Google Scholar 

  • Bentler, P. M. (1972). A lower bound for the dimension-free measurement of internal consistency.Social Science Research, 1, 343–357.

    Google Scholar 

  • Bentler, P. M., & Woodward, J. A. (1980). Inequalities among lower bounds to reliability with applications to test construction and factor analysis.Psychometrika, 45, 249–267.

    Google Scholar 

  • Dunn, G. (1989).Design and analysis of reliability studies. London: Edward Arnold.

    Google Scholar 

  • Guttman, L. (1945). A basis for analyzing test-retest reliability.Psychometrika, 10, 255–262.

    Google Scholar 

  • Lancaster, H. O. (1966). Kolmogorov's remark on the Hotelling canonical correlations.Biometrika, 53, 585–588.

    Google Scholar 

  • Lancaster, H. O. (1969).The chi-squared distribution. New York: John Wiley & Sons.

    Google Scholar 

  • Lehmann, E. L. (1983).Theory of point estimation. New York: John Wiley & Sons.

    Google Scholar 

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

    Google Scholar 

  • Rao, C. R. (1965).Linear statistical inference and its applications. New York: John Wiley & Sons.

    Google Scholar 

  • Renyi, A. (1959). On measures of dependence.Acta Mathematica Academiae Scientiarum Hungaricae, 10, 441–451.

    Google Scholar 

  • Sarmanov, O. V. (1946). Sur les solutions monotones des équations intégrales de corrélation [On monotone solutions of the integral equations of correlation].Doklady Akademii. nauk. SSSR, 53, 781–784.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Statistics Department, London School of Economics and Political Science, Houghton Street, WC2A 2AE, London, England

    M. Knott & D. J. Bartholomew

Authors
  1. M. Knott
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. J. Bartholomew
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Knott, M., Bartholomew, D.J. Constructing measures with maximum reliability. Psychometrika 58, 331–338 (1993). https://doi.org/10.1007/BF02294579

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02294579

Key words

Search

Navigation