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Ordinal Data: An Alternative Distribution

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.
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Abstract

To date, virtually all techniques appropriate for ordinal data are based on the uniform probability distribution over the permutations. In this paper we introduce and examine an alternative probability model for the distribution of ordinal data. Preliminary to deriving the expectations of Spearman's rho and Kendall's tau under this model, we show how to compute certain conditional expectations of rho and tau under the uniform distribution. The alternative probability model is then applied to ordinal test theory, and the calculation of true scores and test reliability are discussed.

Keywords

ordinal datapermutation distributionrank correlationordinal testtrue scorereliability
Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 1 , March 1979 , pp. 3 - 20
Copyright
Copyright © 1979 The Psychometric Society

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