Evaluating the magnitude of differential item functioning in polytomous items

Several recent studies have investigated the application of statistical inference procedures to the analysis of differential item functioning (DIF) in polytomous test items that are scored on an ordinal scale. Mantel's extension of the Mantel-Haenszel test is one of several hypothesis-testing methods for this purpose. The development of descriptive statistics for characterizing DIF in polytomous rest items has received less attention. As a step in this direction, two possible standard error formulas for the polytomous DIF index proposed by Dorans and Schmitt were derived. These standard errors, as well as associated hypothesis-testing procedures, were evaluated though application to simulated data. The standard error that performed better is based on Mantel's hypergeometric model. The alternative standard error, based on a multinomial model, tended to yield values thar were too small.