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The Relative Error Magnitude in Three Measures of Change

Published online by Cambridge University Press:  01 January 2025

Donald W. Zimmerman  and
Richard H. Williams
Donald W. Zimmerman*
Affiliation:
Carleton University
Richard H. Williams
Affiliation:
University of Miami
*
Requests for reprints should be sent to: Donald W. Zimmerman, Department of Psychology, Carleton University, Ottawa, Canada K1S 5B6.
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Abstract

Formulas for the standard error of measurement of three measures of change—simple difference scores, residualized difference scores, and the measure introduced by Tucker, Damarin, and Messick—are derived. Equating these formulas by pairs yields additional explicit formulas which provide a practical guide for determining the relative error of the three measures in any pretest-posttest design. The functional relationship between the standard error of measurement and the correlation between pretest and posttest observed scores remains essentially the same for each of the three measures despite variations in other test parameters (reliability coefficients, standard deviations), even when pretest and posttest errors of measurement are correlated.

Keywords

difference scoresgain scoresresidualized differencesTucker-Damarin-Messick measures
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 2 , June 1982 , pp. 141 - 147
Copyright
Copyright © 1982 The Psychometric Society

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