This article reviews three topics from test theory that continue to raise discussion and controversy and capture test theorists' and constructors' interest. The first topic concerns the discussion of the methodology of investigating and establishing construct validity; the second topic concerns reliability and its misuse, alternative definitions…

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)