This indicates that an examinee's score is conditional on grouping such that having information about group membership changes the probability of a correct response. Therefore, if the groups differ on θ, and performance depends on θ, then the above equation would suggest item bias even in the absence of DIF. For this reason, it is generally agreed upon in the measurement literature that differences on Y conditional on group membership alone is inadequate for establishing bias. In fact, differences on θ or ability are common between groups and establish the basis for much research. Remember to establish bias or DIF, groups must be matched on θ and then demonstrate differential probabilities on Y as a function of group membership.