The Role of the Unit of Analysis in Dimensionality Assessment

A variety of techniques exist for addressing the fundamental question: What does a test measure? The answer to that question often depends on how one asks the question of the data. At one extreme, we see correlations of a test with other editions of that test (e.g., parallel form reliability estimates). At the other extreme, we see exploratory factor analyses of item‐level data. In this paper, we argue that item‐level and test‐score dimensionality are not necessarily identical, define mathematical relationships among item‐level factors, test‐score factors and parcel‐level factors, and advocate that the choice of dimensionality technique should be based on the purpose of the dimensionality analysis. Finally, we illustrate how different approaches yield different answers with SAT‐Verbal data.