Standard Error Estimation for Subpopulation Non-invariance

Score linking is widely used to place scores from different assessments, or the same assessment under different conditions, onto a common scale. A central concern is whether the linking function is invariant across subpopulations, as violations may threaten fairness. However, evaluating subpopulation differences in linked scores is challenging because linking error is not independent of sampling and measurement error when the same data are used to estimate the linking function and to compare score distributions. We show that common approaches involving neglecting linking error or treating it as independent substantially overestimate the standard errors of subpopulation differences. We introduce new methods that account for linking error dependencies. Simulation results demonstrate the accuracy of the proposed methods, and a practical example with real data illustrates how improved standard error estimation enhances power for detecting subpopulation non-invariance.