Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-07T16:01:50.654Z Has data issue: false hasContentIssue false
  • English
  • Français

Individual Distributions Under Ordinal Measurement

Published online by Cambridge University Press:  01 January 2025

Robert S. Schulman
Robert S. Schulman*
Affiliation:
Virginia Polytechnic Institute and State University
*
Requests for reprints should be sent to Robert S. Schulman, Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.
Get access Rights & Permissions [Opens in a new window]

Abstract

For ordinal measurement the concept of an individual propensity distribution is developed. For any given individual the mean of this distribution is his true score, for which estimation procedures are discussed. Two measures of individual dispersion are considered and their distributions derived in the null case. These measures are shown to be counterparts at the individual level of Kendall’s tau and Spearman’s rho. Estimation of the two dispersion measures from sample data is investigated, and the relation of these estimates to the variance of the individual propensity distribution is derived.

Keywords

ordinal testtrue scoreordinal dispersionrank correlation
Type
Article
Information
Psychometrika , Volume 43 , Issue 1 , March 1978 , pp. 19 - 29
Copyright
Copyright © 1978 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

Cochran, W. G. Sampling techniques, 1963, New York: John Wiley & Sons, Inc..Google Scholar
Daniels, H. E. Note on Durbin and Stuart’s formula for E(R s). Journal of the Royal Statistical Society, Series B, 1951, 13, 310–310.CrossRefGoogle Scholar
Durbin, J. & Stuart, A. Inversions and rank correlation coefficients. Journal of the Royal Statistical Society, Series B, 1951, 13, 303–309.CrossRefGoogle Scholar
Kendall, M. G. Rank correlation methods, 1970, London: Charles Griffin & Company.Google Scholar
Lord, F. M. & Novick, M. R. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Schulman, R. S. Correlation and prediction in ordinal test theory. Psychometrika, 1976, 41, 329–340.CrossRefGoogle Scholar
Schulman, R. S. & Haden, R. L. A test theory model for ordinal measurements. Psychometrika, 1975, 40, 455–472.CrossRefGoogle Scholar