Consider the instance where the conditional probability of Y is not the same for the reference and focal groups. In other words, members of different groups with the same trait or ability level have unequal probability distributions on Y. Once controlling for θ, there is a clear dependency between group membership and performance on an item. For dichotomous items, this suggests that when the focal and reference groups are at the same location on θ, there is a different probability of getting a correct response or endorsing an item. Therefore, the group with the higher conditional probability of correctly responding to an item is the group advantaged by the test item. This suggests that the test item is biased and functions differently for the groups, therefore exhibits DIF.