On the Benefits of Using Maximal Reliability in Educational and Behavioral Research.

Abstract

This note is concerned with the benefits that can result from the use of the maximal reliability and optimal linear combination concepts in educational and psychological research. Within the widely used framework of unidimensional multi-component measuring instruments, it is demonstrated that the linear combination of their components that possesses the highest possible reliability can exhibit a level of consistency considerably exceeding that of their overall sum score that is nearly routinely employed in contemporary empirical research. This optimal linear combination can be particularly useful in circumstances where one or more scale components are associated with relatively large error variances, but their removal from the instrument can lead to a notable loss in validity due to construct underrepresentation. The discussion is illustrated with a numerical example.