We contribute to debate about causal inferences in educational research in two ways. First, we quantify how much bias there must be in an estimate to invalidate an inference. Second, we utilize Rubin's causal model to interpret the bias necessary to invalidate an inference in terms of sample replacement. We apply our analysis to an inference…

When attempting to determine if an intervention has a causal impact, the "gold standard" of program evaluation is the randomized controlled trial (RCT). In education studies random assignment is rarely feasible at the student level, making RCTs harder to conduct. School-level assignment is more common but this often requires considerable resources…