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Coefficients Alpha and Reliabilities of Unrotated and Rotated Components

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge  and
Willem K. B. Hofstee
Jos M. F. ten Berge*
Affiliation:
University of Groningen
Willem K. B. Hofstee
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M.F. ten Berge, Heijmans Institute of Psychological Research, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

It has been shown by Kaiser that the sum of coefficients alpha of a set of principal components does not change when the components are transformed by an orthogonal rotation. In this paper, Kaiser's result is generalized. First, the invariance property is shown to hold for any set of orthogonal components. Next, a similar invariance property is derived for the reliability of any set of components. Both generalizations are established by considering simultaneously optimal weights for components with maximum alpha and with maximum reliability, respectively. A short-cut formula is offered to evaluate the coefficients alpha for orthogonally rotated principal components from rotation weights and eigenvalues of the correlation matrix. Finally, the greatest lower bound to reliability and a weighted version are discussed.

Keywords

reliabilitycoefficient alphacomponentsfactorsrotationgreatest lower bound to reliability
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 1 , March 1999 , pp. 83 - 90
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

Comments by Henk A.L. Kiers and by anonymous referees are gratefully acknowledged.

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