An IRT approach for the definition of quantitative variables. Assessing knowledge at University level

The aim of this article is the application of specific models in the context of the IRT approach for the construction of quantitative variables. A model (Equation 4) is considered (Andrich, 1985), deriving from the SLM by Rasch (1960/1980), which allows a reduction of the number of parameters required to represent a set of dichotomous scored responses. An important aspect of this approach is the possibility of examining the difficulties of items in relation to both the whole set of items and how they operate when clustered in subtests. A dispersion parameter, describing the variability of responses to items of each subtest, can also be estimated. Such parameter is also interpreted in terms of dependence among the subtests. In this study, the model of Equation 4 was applied to a set of items dealing with Psychometrics problems; the items were submitted to 140 students, attending a first year course in Psychometrics at the University of Padova. The items, clustered a priori in three areas: Measurement (M), Probability (P), Inference (I), were examined in order to define their specificity in terms of difficulty and dispersion. The difficulty estimates allowed the ordering of the three subtests. Concerning dispersion, subtests M and I can be considered as units since their dispersion parameters were sufficiently low. For subtest P, the dispersion was instead rather high.