Scale matters: Patterns of inequity in measures of structural racism can reverse direction when using the relative vs. the absolute scale.

Quantifying the effect of structural racism on health is a subject of sustained interest. To measure structural racism, analysts often calculate contrasts between marginalized and privileged groups on measures of social determinants in health. These contrasts are predominantly calculated on the relative scale, rather than the absolute scale. In this paper, we investigated the rank ordering of 38 US states in terms of the relative and absolute difference in education and incarceration between Black and White individuals using 2015-2019 data from the American Community Survey and the National Prisoner Statistics. The state-level Black/White ratios and Black-White differences in education were highly correlated (Spearman's rank coefficient = 0.99) and resulted in few rank changes. Conversely, ratios and differences in incarceration were only modestly correlated (Spearman's rank coefficient = 0.43), and resulted in thirteen rank changes of ten or more positions. For incarceration, broad trends in state ordering reverse when considering differences rather than ratios. We contend that for incarceration, the absolute difference is the more meaningful contrast, as it counts the number of additional Black individuals incarcerated. For education, the decision between the relative and absolute scale matters less since the differences and ratios are so highly aligned that states generally fare the same regardless of the measure chosen. Before linking measures of structural racism to health outcomes, researchers are advised to decide the scale for each measure based on conceptual theory and an explicit value judgement.