A note on using stratified alpha to estimate the composite reliability of a test composed of interrelated nonhomogeneous items

The relationship between stratified alpha (alpha(s)) and the reliability of a test composed of interrelated nonhomogeneous items is examined. It is mathematically demonstrated that when there is congeneric equivalence within the strata or subtests, the difference between the coefficients is a function of the variances of the loadings within the strata. When the items within each stratum are essentially tau equivalent, these variances are 0, and alpha(s) and true reliability are equal, provided errors of measurement are uncorrelated. If errors of measurement are positively correlated and there is essential tau equivalence within strata, stratified alpha will overestimate reliability. These findings indicate that recent studies involving stratified alpha (A. Kamata, A. Turhan, & E. Darandari, 2003; H. G. Osburn, 2000) need to be interpreted with some degree of caution. Nevertheless, the hypothetical population data presented in this article suggest that under certain circumstances, stratified alpha can be considerably greater than alpha and closer to the true reliability. Because the former is easily computed, it is recommended that with stratified tests, practicing researchers should routinely calculate both alpha and stratified alpha coefficients.