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A Relationship between Harris Factors and Guttman’s Sixth Lower Bound to Reliability

Published online by Cambridge University Press:  01 January 2025

W. Alan Nicewander
W. Alan Nicewander*
Affiliation:
University of Oklahoma
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Abstract

Using an approach nearly identical to one adopted by Guttman, it is established that within the framework of classical test theory the squared multiple correlation for predicting an element of a composite measure from the n − 1 remaining elements is a lower-bound to the reliability of the element. The relationship existing between the reliabilities of the elements of a composite measure and their squared-multiple correlations with remaining elements is used to derive Guttman’s sixth lower bound (λ6) to the reliability of a composite measure. It is shown that Harris factors of a correlation matrix R are associated with a set of (observable) uncorrelated latent variables having maximum coefficients λ6.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 2 , June 1975 , pp. 197 - 203
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

*

Parts of this paper were presented at the Spring Psychometric Society Meetings, Stanford University, March, 1974.

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