Skip to main content
SpringerLink
Log in

Improving the metric quality of questionnaire data

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

A procedure is proposed whereby questionnaire data, which is usually ordinal in nature and often error-ridden, may be transformed to reduce the error variance in the data and to improve the metric properties of the individual variables. The technique is suggested by a result of Eckart and Young. The properties of the method are investigated by means of a Monte Carlo study. Various matrices were generated representing the usual concept of “true scores”. These matrices were distorted using two levels of random errors and two kinds of categorization. The distorted matrices were in turn transformed by the proposed methods and compared to the “true scores”. In all cases an overall measure of similarity reveals the transformed matrices are better approximations to the “true scores” than the untransformed data. Some properties of the transformation are discussed and some possible applications of the general technique are suggested.

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

  • Burket, G. R., A study of reduced rank models for multiple prediction.Psychometric Monographs, 1964, No. 12.

  • Dawes, R. M., Suppose we measured height with rating scales instead of rulers. Oregon Research Institute Technical Report, Vol. 11, No. 1, 1971.

  • Eckart, C. and Young, G., The approximation of one matrix by another of lower rank.Psychometrika, 1936,1, 211–218.

    Google Scholar 

  • Horn, J. L., A rationale and test for the number of factors in factor analysis.Psychometrika, 1965,30, 179–185.

    Google Scholar 

  • Johnson, R. M., On a theorem stated by Eckart and Young.Psychometrika, 1963,28, 259–264.

    Google Scholar 

  • Labovitz, S., The assignment of numbers to rank order categories.American Sociological Review, 1970,35, 515–524.

    Google Scholar 

  • Pfanzagl, J.,Theory of Measurement. New York: Wiley, 1967.

    Google Scholar 

  • Suppes, P. and Zinnes, J. L., Basic Measurement Theory. In R. D. Luce, R. R. Bush, and E. Galanter (eds.)Handbook of Mathematical Psychology, Vol. 1, New York: Wiley, 1963, pp. 1–76.

    Google Scholar 

  • Wilson, T. P., Critique of ordinal variables.Social Forces, 1970,49, 432–444.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Carnegie-Mellon University, USA

    Terry C. Gleason & Richard Staelin

Authors
  1. Terry C. Gleason
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard Staelin
    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

Gleason, T.C., Staelin, R. Improving the metric quality of questionnaire data. Psychometrika 38, 393–410 (1973). https://doi.org/10.1007/BF02291662

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02291662

Keywords

Search

Navigation