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Reliability and Expected Loss: A Unifying Principle

Published online by Cambridge University Press:  01 January 2025

Bruce Cooil  and
Roland T. Rust
Bruce Cooil*
Affiliation:
Owen Graduate School of Management, Vanderbilt University
Roland T. Rust
Affiliation:
Owen Graduate School of Management, Vanderbilt University
*
Requests for reprints should be sent to Bruce Cooil, Owen Graduate School of Management, Vanderbilt University, 401 21st Avenue South, Nashville, TN 37203.
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Abstract

We provide a unified, theoretical basis on which measures of data reliability may be derived or evaluated, for both quantitative and qualitative data. This approach evaluates reliability as the “proportional reduction in loss” (PRL) that is attained in a sample by an optimal estimator. The resulting measure is between 0 and 1, linearly related to expected loss, and provides a direct way of contrasting the measured reliability in the sample with the least reliable and most reliable data-generating cases. The PRL measure is a generalization of many of the commonly-used reliability measures.

We show how the quantitative measures from generalizability theory can be derived as PRL measures (including Cronbach's alpha and measures proposed by Winer). For categorical data, we develop a new measure for the general case in which each of N judges assigns a subject to one of K categories and show that it is equivalent to a measure proposed by Perreault and Leigh for the case where N is 2.

Keywords

alphakappaagreementintercoder reliabilitydecision rulegeneralizability theorytest theory
Type
Original Paper
Information
Psychometrika , Volume 59 , Issue 2 , June 1994 , pp. 203 - 216
Copyright
Copyright © 1994 The Psychometric Society

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Footnotes

Bruce Cooil is an Associate Professor of Statistics, and Roland T. Rust is a Professor and area head for Marketing. The authors thank three anonymous reviewers and an Associate Editor for their helpful comments and suggestions. This work was supported in part by the Dean's Fund for Faculty Research of the Owen Graduate School of Management, Vanderbilt University.

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