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On the Reliability of a Weighted Composite

Published online by Cambridge University Press:  01 January 2025

Charles I. Mosier
Charles I. Mosier*
Affiliation:
Social Security Board
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Abstract

A general formula for the reliability of a weighted composite has been derived by which that reliability can be estimated from a knowledge of the weights whatever their source, reliabilities, dispersions, and intercorrelations of the components. The Spearman-Brown formula has been shown to be a special case of the general statement. The effect of the internal consistency or intercorrelation of the components has been investigated and the conditions defining the set of weights yielding maximum reliability shown to be that the weight of a component is proportional to the sum of its intercorrelations with the remaining components and inversely proportional to its error variance.

Type
Original Paper
Information
Psychometrika , Volume 8 , Issue 3 , September 1943 , pp. 161 - 168
Copyright
Copyright © 1943 The Psychometric Society

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Footnotes

*

The opinions expressed in this article are those of the author and do not necessarily reflect the official views of the Social Security Board.

References

† Certain of the deductions set forth in this paper are implicit in Kelley, T. L., Statistical Method, Chapter IX, and others in Richardson, M. W. “The Combination of Measures,” in Horst, Paul, The Prediction of Personal Adjustment, Social Science Research Council, 1941.

* Kelley, T. L., The Reliability Coefficient, Psychomctrika, 1942, 7, 75-83.

† On this, cf. Richardson, M. W. “The combination of messares.” In Horst, Paul, The Prediction of Personal Adjustment, Social Science Research Council, 1941, especially pp. 392 and 397.