A Comparison of Lord's Chi-Square, Raju's Area Measures, and the Likelihood Ratio Test on Detection of Differential Item Functioning

This study compares three procedures for the detection of differential item functioning (DIF) under item response theory (IRT): (a) Lord's chi-square, (b) Raju's area measures, and (c) the likelihood ratio test. Relations among the three procedures and some practical considerations, such as linking metrics and scale purification, are discussed. Data from two forms of a university mathematics placement test were analyzed to examine the congruence among the three procedures. Results indicated that there was close agreement among the three DIF detection procedures.