Determining the significance of estimated signed and unsigned areas between two item response functions

Abstract

Asymptotic sampling distributions (means and variances) of estimated signed and unsigned areas between two item response functions (IRFS) are presented for the Rasch model, the two-parameter model, and the three-parameter model with fixed lower asymptotes. In item bias or differential item functioning research, it may be of interest to determine whether the estimated signed and unsigned areas between IRFS calibrated with two different groups are significantly different from 0. The usefulness of these sampling distributions in this context is discussed and illustrated. More empirical research with the proposed significance tests is necessary. Index terms: asymptotic mean and variance, differential item functioning, item bias, item response functions, item response theory.