Differential item functioning (DIF) 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. DIF analysis provides an indication of unexpected behavior by item 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 people from different groups of same underlying true ability have a different probability to give a certain response. More precisely, an item displays DIF when the difficulty level (b), the discrimination (a) or the lower asymptotes (c) – estimated by item response theory

Item response theory

In psychometrics, item response theory also known as latent trait theory, strong true score theory, or modern mental test theory, is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. It is based...

 (IRT) – of an item differs across groups. Thus, when one or more item parameters differ across groups, an item displays DIF.

The Mantel–Haenszel and logistic regression

Logistic regression

In statistics, logistic regression is used for prediction of the probability of occurrence of an event by fitting data to a logit function logistic curve. It is a generalized linear model used for binomial regression...

procedures are the most widely used methods to investigate DIF. Zumbo (2007) offers a review of various DIF detection methods and strategies.