Examining change in maximal reliability for multiple-component measuring instruments

A method for examining change in maximal reliability for pre-specified sets of congeneric measures when developing a multi-component instrument is outlined. The approach is applicable for purposes of estimation and testing of gain or loss in the maximal reliability coefficient as a consequence of adding or dropping one or more measures from a homogeneous composite with uncorrelated errors, as well as when one is concerned with optimal component choice for highest increase or correspondingly smallest drop in maximal reliability. The method is compared with a procedure for ascertaining change in unweighted sum score reliability, and implications for instrument construction and revision are discussed. The approach is illustrated with a numerical example.