Differential item functioning

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Differential item functioning (DIF) occurs when people from different groups (commonly gender or ethnicity) with the same latent trait (the same ability/skill) have a different probability of giving a certain response on a questionnaire or test. DIF analysis (often the Mantel Haenszel procedure is used) provides an indication of unexpected behavior by item on a test. An item doesn’t display DIF if people from different groups have a different probability to give a certain response; it displays DIF if people from different groups in spite of their same underlying true ability have a different probability to give a certain response. More precisely, an item displays DIF when the difficulty level (β), the discrimination (α) or the lower asymptotes (γ) -estimated by item response theory (IRT)- of an item differs across groups. Thus, when one or more item parameters differ across groups, an item displays DIF.

Often, reviewing individual items showing DIF will result in no clear explanation for the difference in performance between different groups - males and females for instance. It is often most useful to look at groups of items showing DIF and draw conclusions about common features of these items - content, grammatical structure, and cognitive processes involved.

Reference: Embretson,S.E., Reise,S.P. (2000) Item Response Theory for Psychologists.