This discussion paper argues that both the use of Cronbach's alpha as a reliability estimate and as a measure of internal consistency suffer from major problems. First, alpha always has a value, which cannot be equal to the test score's reliability given the inter-item covariance matrix and the usual assumptions about measurement error. Second, in…

The critical reactions of Bentler (2009, doi: 10.1007/s11336-008-9100-1), Green and Yang (2009a, doi: 10.1007/s11336-008-9098-4 ; 2009b, doi: 10.1007/s11336-008-9099-3), and Revelle and Zinbarg (2009, doi: 10.1007/s11336-008-9102-z) to Sijtsma's (2009, doi: 10.1007/s11336-008-9101-0) paper on Cronbach's alpha are addressed. The dissemination of…

Three methods for estimating reliability are studied within the context of nonparametric item response theory. Two were proposed originally by Mokken and a third is developed in this paper. Using a Monte Carlo strategy, these three estimation methods are compared with four "classical" lower bounds to reliability. (Author/JAZ)