The purpose of this article is to examine the role of the unit in physics in order to clarify the role of the unit in psychometrics. Based on this examination, metrological conventions are used to formulate the relationship between discrimination and the unit of a scale in item response theory. Seminal literature in two lines of item response theory is reviewed in light of the standard definition of measurement in physics, and Birnbaum's formulation of the discrimination parameter in item response theory is reexamined. Consequently, the article introduces a scale parameter in a model that specializes to both the two-parameter logistic (2PL) and Rasch models. The model has sufficient statistics for person and item parameters, the feature that defines Rasch models, whilst also parameterizing discrimination. By formulating the relationship between discrimination and the unit, this article reconciles differing perspectives regarding the use of a discrimination parameter in the 2PL and Rasch models. A simulation study is used to demonstrate the results of implementing conditional maximum likelihood estimations of item locations. Implications for the progress of measurement in the social sciences are identified and discussed. It is argued that these implications entail substantial shifts in the way we think about measurement in the social sciences.