Effect of Choice of Measure on the Size of a Racial Disparity - Langan, Patrick A. (Journal of quantitative criminology, 2001)
In criminological studies of racial disparities the effect of race on outcomes is assessed after statistical controls for other variables. There is no universally accepted measure of size of disparity after controls in the most common type of disparity study: the study of binary outcomes. Some such studies use a measure that lends itself to interpretation in terms of the proportional reduction in error (PRE). Most use a non-PRE measure of association. This study investigates the effect of choice of measure on conclusions about the size of a disparity after controls. For illustrative purposes the study analyzes data on the awarding of sentence reductions to drug traffickers. After controls, blacks are found to be substantially less likely than whites to receive a reduction according to a type of non-PRE measure: an odds ratio derived from a logit model. But using the same data and model, PRE measures obtained from an ROC analysis indicate that, after controls, there is hardly any difference between the races in their likelihood of sentence reduction. Results illustrate the study's thesis: that the choice of measure can powerfully affect conclusions. The findings' implications—for policymakers and for researchers who conduct racial disparity studies—are discussed.