Test Score Measurement and the Black-White Test Score Gap

Research as to the size of the black-white test score gap often comes to contradictory conclusions. Recent literature has affirmed that the source of these contradictions and other controversies in education economics may be due to the fact that test scores contain only ordinal information. In this paper, I propose a normalization of test scores that is invariant to monotonic transformations. Under fairly weak assumptions, this metric has interval properties and thus solves the ordinality problem. The measure can serve as a valuable robustness check to ensure that any results are not simply statistical artifacts from the choice of scale.