Lord's Paradox and Targeted Interventions: The Case of Special Education
Advisors: Thomas Richardson and Dan Goldhaber Lord (1967) describes a hypothetical â€œparadoxâ€ in which two statisticians, analyzing the same dataset using different but defensible methods, come to very different conclusions about the effects of an intervention on student outcomes. I use graphical methodsâ€”including a new graphical framework called Single World Object Oriented Plates (SWOOPs)â€”and detailed, longitudinal data about all public school students in Washington State to investigate a real-life example of Lordâ€™s Paradox that arises in evaluating the impact of special education services on student performance. From this discussion and a corresponding replication study, I conclude that methods employed in existing studies of special education (Hanushek et al., 2002; Morgan et al., 2010) may lead to biased estimates, but in opposite directions. I then introduce an instrumental variables (IV) approach that exploits a threshold in the stateâ€™s special education funding laws that caps per-pupil special education funding at 12.7% of a districtâ€™s students, and use SWOOPs to argue that the assumptions that justify this approach are more plausible than the assumptions that justify the methods from Hanushek et al. (2002) and Morgan et al. (2010). I find that students in districts that pass this threshold are far less likely to be placed in special education, all else equal, and use a districtâ€™s position relative to this funding threshold as an instrumental variable to estimate the average treatment effect of special education services on student test performance.