How to Compare Parametric and Nonparametric Person‐Fit Statistics Using Real Data

Abstract Person‐fit assessment (PFA) is concerned with uncovering atypical test performance as reflected in the pattern of scores on individual items on a test. Existing person‐fit statistics (PFSs) include both parametric and nonparametric statistics. Comparison of PFSs has been a popular research topic in PFA, but almost all comparisons have employed simulated data. This article suggests an approach for comparing the performance of parametric and nonparametric PFSs using real data. This article then shows that there is no clear winner between , a popular parametric PFS, and , a popular nonparametric statistic, in a comparison using the suggested approach. This finding is contradictory to the common finding shown by Karabatsos, Dimitrov and Smith, and Tendeiro and Meijer that is more powerful than several parametric PFSs including and .