Test scores’ robustness to scaling: The scale_transformation command

Social scientists frequently rely on the cardinal comparability of test scores to assess achievement gaps between population subgroups and their evolu- tion over time. This approach has been criticized because of the ordinal nature of test scores and the sensitivity of results to order-preserving transformations that are theoretically plausible. Bond and Lang (2013, Review of Economics and Statistics 95: 1468–1479) document the sensitivity of measured ability to scaling choices and develop a method to assess the robustness of changes in ability over time to scaling choices. In this article, I present the scale_transformation com- mand, which expands the Bond and Lang (2013) method to more general cases and optimizes their algorithm to work with large datasets. The command assesses the robustness of an achievement gap between two subgroups to any arbitrary choice of scale by finding bounds for the original gap estimation. Additionally, it finds scale transformations that are very likely and unlikely to benchmark against the results obtained. Finally, it also allows the user to measure how much gap growth coefficients change when including controls in their specifications.