In calibration experiments, an estimated relationship between covariate information for a sample and an observed response is used to infer the covariate information for unknown samples from their responses. In some situations, this covariate information comprises a nominal variable (e.g., identity of a chemical, sex of an animal) and a real-valued variable (e.g., concentration of the chemical, age of animal). If the calibrating relationship can be estimated separately for each candidate identity, the first step in analyzing unknown samples is to correctly determine their identity. A discrimination statistic is suggested for use in this situation and its asymptotic distribution is derived. The investigation is motivated by the possibility of using multiple immunoassays in environmental monitoring to identify and quantitate contaminated samples in situations where there are several candidate pollutants that cross-react significantly to single assays. An example is given of the use of a four-antibody assay for the simultaneous monitoring of the levels in water samples of several of the commonly used triazine herbicides and their derivatives.