Analytical Solution for the Optimal Addition of an Item to a Composite of Scores for Maximum Reliability

Abstract

This paper presents a derivation of the optimal weight to be assigned for an item so that it maximally increases the reliability of the aggregate. This aggregate is the best estimate of the underlying true repeating pattern. The approach differs from previous solutions in being analytical, based on the Signal to Noise Ratio (SNR) instead of the reliability itself, and the ability to visually inform the researcher about the relevance of the weighting strategy and the gains produced in the SNR. Optimal weighting of repetitive phenomena is a bonus not only in the behavioral sciences, but also in many engineering fields. Its uses may include the selection or discarding of raters, judges, repetitions, or epochs, depending on the field.