Weights That Maximize Reliability Under a Congeneric Model

Abstract

In many measurement situations, it is often desirable to weight different scores to form a composite score. The desire to maximize the reliability of the composite score is an important factor in determining the weights. Current procedures are computationally complex and usually require information, not always readily available, about the reliability of each part score. Equations for computing weights that maximize the reliability of a test with multiple parts were derived using a congeneric model. A direct derivation for the three-part case and a two-step derivation for the n-part case are presented, and results for these two approaches were shown to be consistent for the three-part case. The computations are relatively simple and are based on the variance-covariance matrix of the part scores. Two examples are given to show the computations and the usefulness of the equations.