A comparison of two area measures for detecting differential item functioning

Abstract

The area between two item response functions is often used as a measure of differential item functioning under item response theory. This area can be measured over either an open interval (i.e., exact) or closed interval. Formulas are presented for computing the closed-interval signed and unsigned areas. Exact and closed-interval measures were estimated on data from a test with embedded items intentionally constructed to favor one group over another. No real differences in detection of these items were found between exact and closed-interval methods. Index terms: BILOG, closed interval, differential item functioning, item response functions, open interval, signed area, unsigned area.