A Nonparametric Item Characteristic Curve using the Gini's Mean Difference

The Item Characteristic Curve describes the relationship between the probability of correctly answering a question and the ability presumed to be required to answer the question. Since ability is a latent variable, distributional assumptions must be imposed on it in order to estimate such relationship. In this paper we overcome the need to impose an assumption on the distribution of abilities by using the properties of concentration curves and Gini's Mean Difference (GMD). This enables investigation of whether the probability of correctly answering a question is monotonically related to a specific ability. The method is also useful for classifying abilities. This paper details the properties of the technique and provides examples of its application