Attenuation-Corrected Estimators of Reliability

Abstract

<p>The estimates of reliability are usually attenuated and deflated because the item–score correlation (ρgXρgX, <em>Rit</em>) embedded in the most widely used estimators is affected by several sources of mechanical error in the estimation. Empirical examples show that, in some types of datasets, the estimates by traditional alpha may be deflated by 0.40–0.60 units of reliability and those by maximal reliability by 0.40 units of reliability. This article proposes a new kind of estimator of correlation: attenuation-corrected correlation (<em>R</em>_<em>AC</em>): the proportion of observed correlation with the maximal possible correlation reachable by the given item and score. By replacing ρgXρgX with <em>R</em>_<em>AC</em> in known formulas of estimators of reliability, we get attenuation-corrected alpha, theta, omega, and maximal reliability which all belong to a family of so-called deflation-corrected estimators of reliability.<br></p>