Using Three Different Categorical Data Analysis Techniques to Detect Differential Item Functioning

Diversity in the population along with the diversity of testing usage has resulted in smaller identified groups of test takers. In addition, computer adaptive testing sometimes results in a relatively small number of items being used for a particular assessment. The need and use for statistical techniques that are able to effectively detect differential item functioning (DIF) when the population is small and or the assessment is short is necessary. Identification of empirically biased items is a crucial step in creating equitable and construct-valid assessments. Parshall and Miller (1995) compared the conventional asymptotic Mantel-Haenszel (MH) with the exact test (ET) for the detection of DIF with small sample sizes. Several studies have since compared the performance of MH to logistic regression (LR) under a variety of conditions. Both Swaminathan and Rogers (1990), and Hildalgo and López-Pina (2004) demonstrated that MH and LR were comparable in their detection of items with DIF. This study followed by comparing the performance of the MH, the ET, and LR performance when both the sample size is small and test length is short. The purpose of this Monte Carlo simulation study was to expand on the research done by Parshall and Miller (1995) by examining power and power with effect size measures for each of the three DIF detection procedures. The following variables were manipulated in this study: focal group sample size, percent of items with DIF, and magnitude of DIF. For each condition, a small reference group size of 200 was utilized as well as a short, 10-item test. The results demonstrated that in general, LR was slightly more powerful in detecting items with DIF. In most conditions, however, power was well below the acceptable rate of 80%. As the size of the focal group and the magnitude of DIF increased, the three procedures were more likely to reach acceptable power. Also, all three procedures demonstrated the highest power for the most discriminating item. Collectively, the results from this research provide information in the area of small sample size and DIF detection