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

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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.