Congeneric and (Essentially) Tau-Equivalent Estimates of Score Reliability What They Are and How to Use Them

• Published in: Educational and psychological measurement Vol. 66; no. 6; pp. 930 - 944
• Main Author: Graham, James M.
• Format: Journal Article
• Language: English
• Published: Thousand Oaks, CA SAGE Publications 01-12-2006; Sage
• Subjects: Biological and medical sciences; Error of Measurement; Fundamental and applied biological sciences. Psychology; Goodness of Fit; Heuristics; Internal Consistency; Mathematical Models; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics; Psychometrics. Statistics. Methodology; Reliability; Researchers; Scores; Statistics. Mathematics; Structural Equation Models; Test Items; Test Theory; congeneric; tau-equivalent; structural equation modeling; reliability; Statistical method; Structural equation modeling; Psychometrics; Test reliability
• ISSN: 0013-1644; 1552-3888
• DOI: 10.1177/0013164406288165

Coefficient alpha, the most commonly used estimate of internal consistency, is often considered a lower bound estimate of reliability, though the extent of its underestimation is not typically known. Many researchers are unaware that coefficient alpha is based on the essentially tau-equivalent measurement model. It is the violation of the assumptions required by this measurement model that are often responsible for coefficient alpha's underestimation of reliability. This article presents a hierarchy of measurement models that can be used to estimate reliability and illustrates a procedure by which structural equation modeling can be used to test the fit of these models to a set of data. Test and data characteristics that can influence the extent to which the assumption of tau-equivalence is violated are discussed. Both heuristic and applied examples are used to augment the discussion.