Two-Stage Equating in Differential Item Functioning Detection under the Graded Response Model with the Raju Area Measures and the Lord Statistic

The differential item functioning (DIF) detection in polytomous response items is an area of study of recent interest. Cohen and colleagues proposed a polytomous extension of the Lord statistic and the Raju exact area measures, when the items fit the graded response model. This study examined the effects of test purification in detecting DIF by means of polytomous extensions of the Raju area measures and the Lord statistic. The factors manipulated were percentage of DIF items in the test (5%, 10%, and 20%), amount of DIF (0.2, 0.4, and 0.8), sample size (250, 500, and 1,000) and test purification (noniterative versus two-stage). The results of this study suggest that the use of the two-stage equating procedure with Z(SA) and χ2-LORD reduces the percentage of false positives and improves the detection of DIF.