The first section of this paper defines three incompatible ethical positions in regard to the fair and unbiased use of psychological tests for selection in minority and majority groups. Also in this section, five statistical definitions of "test fairness" are reviewed and examined critically for technical, logical, and social weaknesses. In the second section of the paper, the various statistical definitions are shown to correlate with specific ethical positions, and the technical, logical, and social problems of each statistical model-ethical position combination are delineated. It is concluded that it is difficult, if not impossible, to predict at the present time which model will ultimately prove most acceptable to the American people. (Author)