1. Differential Item Functioning (DIF) occurs when individuals from different groups (e.g., gender, ethnicity) with the same underlying ability have different probabilities of answering an item correctly. 2. The problem is to detect whether an item in a test functions differently across groups, which can indicate bias. 3. A common approach uses logistic regression or item response theory (IRT) models to compare item characteristic curves between groups. 4. For logistic regression, the model is $$\log\left(\frac{P}{1-P}\right) = \beta_0 + \beta_1 \text{Ability} + \beta_2 \text{Group} + \beta_3 (\text{Ability} \times \text{Group})$$ where $P$ is the probability of a correct response. 5. Significant $\beta_2$ or $\beta_3$ coefficients indicate uniform or non-uniform DIF respectively. 6. Steps to detect DIF: 1. Estimate ability scores for all individuals. 2. Fit the logistic regression model for each item. 3. Test significance of group and interaction terms. 4. Items with significant terms are flagged for DIF. 7. This method helps ensure fairness in testing by identifying biased items.