On the Integrity of Reliability Estimation in Classical Test Theory: The Case for an Additive Coefficient of Stability

Abstract

This article addresses deficiencies in the most widely used estimators of reliability and draws attention to the reason that this issue is important. Accurate calibration of relationships between constructs is critical to theory development. Unless workers have accurate estimates of scale reliability, accurate estimates of those relationships will not be forthcoming because the classical disattenuation formula requires them. This article shows that classical test theory can easily accommodate the delineation of its error component E in test scores into two sources, inconsistency across content (E1) and inconsistency across time (E2). Viewed from this extended model, the alternate forms approach to reliability estimation is complete in that it gauges simultaneously both sources of error. Because that approach is rarely used today for that purpose, the integrity of estimation has been lost. In its place arose estimators of partial reliability--those for estimating generalizability over one medium or the other, but not both, thereby precluding the additivity of error components. Recent developments promise to restore the integrity of the alternate forms approach without the need for alternate forms and suggest an additive alternative to the current nonadditive coefficient of stability.