How do you define Mantel Haenszel Differential item functioning (DIF)?

What are the the three methods of assessing DIF across multiple demographic group. "a. Mantel-Haenszel chi-square statistics with no adjustment to the alpha level, b. Mantel-Haenszel chi-sqaure with a Bonferroni adjustment alpha level, C. Generalized mantel-Haenszel statistics (GMH) that offers a single test of significance across all groups.

How do you define Mantel Haenszel Differential item functioning (DIF)?
Bias is systematic error that favors one group over another. There are different ways to detect bias. The logical first step in detecting bias is to find elements where one group performs much better than the other group: such items function differentially for the two groups and thus is known as Differential Item Functioning (DIF). DIF is a necessary but not sufficient condition for bias: bias only exists if the difference is illegitimate, i.e., if both groups should be performing equally well on the item. The simplest DIF index is based on the differences in correct response rates between a "reference" and "focal" group.





The Mantel-Haenszel odds ratio is a non-parametric statistic using chi-square. For every score level, it calculates the odds that the reference group will get the item correct, and that the focal group will get it correct. It then divides reference group odds by focal group odds, showing how much more likely the reference group is to get the item correct. You can transform results from the Mantel-Haenszel procedure into its delta


units to classify items into grouped results.





Mantel-Haenszel has two major practical advantages: it is conceptually uncomplicated, and it doesn't require highly specialized software. However, Mantel-Haenszel can be affected by item discrimination and it performs better with large group sizes.

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