Testing programs are often called upon to use their tests for multiple purposes. Alternate uses may include administering the test to groups different from the target population. Whenever the use of a test is expanded by administering it in other than the target population, fairness becomes a major concern. This study illustrates how the evaluation of two psychometric concepts—differential item functioning and linking invariance—can provide useful empirical evidence to assess this extended test use. Data from a large-scale language examination on which test takers were heterogeneous not only in their backgrounds (e.g., language, geographic region) but also in their performance levels were chosen as an example.