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Psychometrika

, Volume 64, Issue 1, pp 83–90 | Cite as

Coefficients alpha and reliabilities of unrotated and rotated components

  • Jos M. F. ten Berge
  • Willem K. B. Hofstee
Article

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.

Key words

reliability coefficient alpha components factors rotation greatest lower bound to reliability 

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Copyright information

© The Psychometric Society 1999

Authors and Affiliations

  • Jos M. F. ten Berge
    • 1
  • Willem K. B. Hofstee
    • 1
  1. 1.Heijmans Institute of Psychological ResearchUniversity of GroningenGroningenThe Netherlands

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