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.
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Mosier, C.I. On the reliability of a weighted composite. Psychometrika 8, 161–168 (1943). https://doi.org/10.1007/BF02288700
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DOI: https://doi.org/10.1007/BF02288700