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differential item functioning
Differential item functioning (DIF), also referred to as measurement bias, occurs when people from different groups (commonly gender or ethnicity) with the same latent trait (ability/skill) have a different probability of giving a certain response on a questionnaire or test.〔Embretson,S. E., Reise,S. P. (2000).''Item Response Theory for Psychologists''. New Jersey: Lawrence Erlbaum.〕 DIF analysis provides an indication of unexpected behavior of items on a test. An item does not display DIF if people from different groups have a different probability to give a certain response; it displays DIF if and only if people from different groups ''with the same underlying true ability'' have a different probability of giving a certain response. Common procedures for assessing DIF are Mantel-Haenszel, item response theory (IRT) based methods, and logistic regression.〔Zumbo, B.D. (2007). Three generations of differential item functioning (DIF) analyses: Considering where it has been, where it is now, and where it is going. ''Language Assessment Quarterly, 4,'' 223–233.〕
==Description ==
DIF refers to differences in the functioning of items across groups, oftentimes demographic, which are matched on the latent trait or more generally the attribute being measured by the items or test.〔Camilli, G. (2006). Test fairness: In R. L. (Ed.), ''Educational measurement'' (4th ed., pp. 220-256). Westport, CT: American Council on Education.〕〔Holland, P. W., & Wainer, H. (1993). ''Differential item functioning.'' Hillsdale, NJ: Lawrence Erlbaum.〕 It is important to note that when examining items for DIF, the groups must be matched on the measured attribute, otherwise this may result in inaccurate detection of DIF. In order to create a general understanding of DIF or measurement bias, consider the following example offered by Osterlind and Everson (2009).〔Osterlind, S. J. & Everson, H. T. (2009). ''Differential item functioning.'' Thousand Oaks, CA: Sage Publishing.〕 In this case, Y refers to a response to a particular test item which is determined by the latent construct being measured. The latent construct of interest is referred to as theta (θ) where Y is an indicator of θ which can be arranged in terms of the probability distribution of Y on θ by the expression ''f''(Y)|θ. Therefore, response Y is conditional on the latent trait (θ). Because DIF examines differences in the conditional probabilities of Y between groups, let us label the groups as the “reference” and “focal” groups. Although the designation does not matter, a typical practice in the literature is to designate the reference group as the group who is suspected to have an advantage while the focal group refers to the group anticipated to be disadvantaged by the test.() Therefore, given the functional relationship ''f''(Y)|θ and under the assumption that there are identical measurement error distributions for the reference and focal groups it can be concluded that under the null hypothesis:
''f'' (Y = 1 | θ, G = r) = ''f'' (Y = 1 | θ, G = f)
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