Reliability and expected loss: A unifying principle

Abstract

We provide a unified, theoretical basis on which measures of data reliability may be derived or evaluated, for both quantitative and qualitative data. This approach evaluates reliability as the “proportional reduction in loss” (PRL) that is attained in a sample by an optimal estimator. The resulting measure is between 0 and 1, linearly related to expected loss, and provides a direct way of contrasting the measured reliability in the sample with the least reliable and most reliable data-generating cases. The PRL measure is a generalization of many of the commonly-used reliability measures. We show how the quantitative measures from generalizability theory can be derived as PRL measures (including Cronbach's alpha and measures proposed by Winer). For categorical data, we develop a new measure for the general case in which each of N judges assigns a subject to one of K categories and show that it is equivalent to a measure proposed by Perreault and Leigh for the case where N is 2.