Components of Variance of Scales With a Bifactor Subscale Structure From Two Calculations of α

Since Cronbach's (1951) elaboration of a from its introduction by Guttman (1945), this coefficient has become ubiquitous in characterizing assessment instruments in education, psychology, and other social sciences. Also ubiquitous are caveats on the calculation and interpretation of this coefficient. This article summarizes a recent contribution (Andrich, 2015) on the use of coefficient a which complements these many caveats. It shows that in the presence of a simple bifactor structure of a scale where unique components of variance are homogeneous in magnitude, three components of variance and the common latent common correlation among the subscales can be calculated from the ratio of two calculations of a, one at the level of the items, the other at the level of the subscales. It was suggested that these two ready calculations and their interpretation, and the reporting of all four indices in the analysis of scales with a subscale structure, would reduce the misinterpretation of this coefficient. An illustrative example of the application of the calculations is also shown.