Examining group differences in reliability of multiple-component instruments

A covariance structure modelling method for examining group differences in scale reliability of multi-component measuring instruments is proposed. The procedure is based on a set of appropriate parameter constraints imposed in a multiple-population structural model. Unlike tests of group differences in coefficient alpha that in general do not evaluate the discrepancies in scale reliability coefficients, the described approach permits one to examine differences in the latter quantities of actual interest when concerned with questions pertaining to reliability of composite scores. The method can be used to test whether a given measuring instrument has identical reliabilities in studied populations, and/or whether distinct instruments, or modes of administration of the same instrument, have equal reliabilities across groups. The proposed procedure is illustrated with a pair of examples.