Coefficient Alpha and Reliability of Scale Scores

The majority of large-scale assessments develop various score scales that are either linear or nonlinear transformations of raw scores for better interpretations and uses of assessment results. The current formula for coefficient alpha (α; the commonly used reliability coefficient) only provides internal consistency reliability estimates of raw scores. This article presents a general form of α and extends its use to estimate internal consistency reliability for nonlinear scale scores (used for relative decisions). The article also examines this estimator of reliability using different score scales with real data sets of both dichotomously scored and polytomously scored items. Different score scales show different estimates of reliability. The effects of transformation functions on reliability of different score scales are also explored.