Nonparametric person-fit research: Some theoretical issues and an empirical example

In person-fit analysis, it is investigated whether an item score pattern is improbable given the item score patterns of the other persons in the group or given an expected score pattern on the basis of a test model. In this study, several existing group-based statistics are discussed to detect such improbable item score patterns, along with the cut scores that were proposed in the literature to classify an item score pattern as aberrant. By means of a simulation study and an empirical study, the detection rate of these statistics is compared, and the practical use of various cut scores is investigated. It is furthermore demonstrated that person-fit statistics can be used to detect persons with a deficiency of knowledge on an achievement test.