Multiple-Component Measurement Instruments in Heterogeneous Populations: Is There a Single Coefficient Alpha?

This note confronts the common use of a single coefficient alpha as an index informing about reliability of a multicomponent measurement instrument in a heterogeneous population. Two or more alpha coefficients could instead be meaningfully associated with a given instrument in finite mixture settings, and this may be increasingly more likely the case in empirical educational and psychological research. It is argued that in such situations explicit examination of class-invariance in the alpha coefficient must precede any statements about its possible value in the studied population. The approach permits also the evaluation of between-class alpha differences as well as point and interval estimation of the within-class alpha coefficients. The method can similarly be used in situations with (a) known class membership when distinct (sub)populations are investigated while their number is known beforehand and membership in them is observed for studied persons, as well as (b) in settings where only the number of latent classes is known for a population under investigation. The outlined procedure is illustrated with numerical data.