Estimation of and Confidence Interval Formation for Reliability Coefficients of Homogeneous Measurement Instruments

Abstract

The reliability of a composite score is a fundamental and important topic in the social and behavioral sciences. The most commonly used reliability estimate of a composite score is coefficient α. However, under regularity conditions, the population value of coefficient α is only a lower bound on the population reliability, unless the items are essentially τ-equivalent, an assumption that is likely violated in most applications. A generalization of coefficient α, termed ω, is discussed and generally recommended. Furthermore, a point estimate itself almost certainly differs from the population value. Therefore, it is important to provide confidence interval limits so as not to overinterpret the point estimate. Analytic and bootstrap methods are described in detail for confidence interval construction for ω. We go on to recommend the bias-corrected bootstrap approach for ω and provide open source and freely available R functions via the MBESS package to implement the methods discussed.