Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T16:46:39.914Z Has data issue: false hasContentIssue false
  • English
  • Français

Improving the Metric Quality of Questionnaire Data

Published online by Cambridge University Press:  01 January 2025

Terry C. Gleason  and
Richard Staelin
Terry C. Gleason
Affiliation:
Carnegie-Mellon University
Richard Staelin
Affiliation:
Carnegie-Mellon University
Get access Rights & Permissions [Opens in a new window]

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.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 3 , September 1973 , pp. 393 - 410
Copyright
Copyright © 1973 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Burket, G. R. A study of reduced rank models for multiple prediction. Psychometric Monographs, 1964, No. 12.Google Scholar
Dawes, R. M. Suppose we measured height with rating scales instead of rulers. Oregon Research Institute Technical Report, Vol. 11, No. 1, 1971.CrossRefGoogle Scholar
Eckart, C. and Young, G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218CrossRefGoogle Scholar
Horn, J. L. A rationale and test for the number of factors in factor analysis. Psychometrika, 1965, 30, 179–185CrossRefGoogle ScholarPubMed
Johnson, R. M. On a theorem stated by Eckart and Young. Psychometrika, 1963, 28, 259–264CrossRefGoogle Scholar
Labovitz, S. The assignment of numbers to rank order categories. American Sociological Review, 1970, 35, 515–524CrossRefGoogle Scholar
Pfanzagl, J. Theory of Measurement, 1967, New York: WileyGoogle Scholar
Suppes, P., and Zinnes, J. L. Basic Measurement Theory. In Luce, R. D., Bush, R. R. and Galanter, E. (Eds.), Handbook of Mathematical Psychology, Vol. 1. New York: Wiley. 1963, 1–76Google Scholar
Wilson, T. P. Critique of ordinal variables. Social Forces, 1970, 49, 432–444CrossRefGoogle Scholar