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A Stochastic Model for Test-Retest Correlations

Published online by Cambridge University Press:  01 January 2025

Donald G. Morrison
Donald G. Morrison*
Affiliation:
Columbia University
*
Requests for reprints should be sent to Donald G. Morrison, Graduate School of Business, Columbia University, New York, New York 10027.
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Abstract

A simple stochastic model is formulated in order to determine the optimal time between the first test and the second test when the test-retest method of assessing reliability is used. A forgetting process and a change in true score process are postulated. The optimal time between tests is derived by maximizing the probability that the respondent has not remembered the response on the first test and has not had a change in true score. The resulting test-retest correlation is then found to be a linear function of the true reliability of the test, where the slope of this function is the key probability of not remembering and having no change in true score. Some numerical examples and suggestions for using the results in empirical studies are given. Specific recommendations are presented for improved design and analysis of intentions data.

Keywords

reliabilityforgettingtrue scoreoptimal time intervalexponential distributionindividual differences
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 2 , June 1981 , pp. 143 - 151
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

This research was made possible by a grant from the Center for Food Policy Research, Graduate School of Business, Columbia University, New York, New York, 10027.

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