Causal inference with binary treatments from randomization versus binary treatments from categorization

The causal inference methods of potential outcomes (POs), directed acyclic graphs (DAGs), and structural equation models (SEMs) have contributed much to our understanding of causal effects. Yet the teaching and application of these methods (especially POs and DAGs) have nearly always regarded treatment as binary even when the magnitude of treatment can differ greatly. The two most common types of binary treatments are those from randomized experiments and those that are categorized versions of continuous treatments. Binary treatments via categorization are far more common in observational studies. I derive results showing that binary treatment variables that have different origins should be treated differently. Not doing so makes biased causal inferences more likely. I illustrate the value of combining POs, DAGs, and SEMs perspectives to illuminate potential problems with binary treatments rather than relying only on one perspective. The new analytic results are illustrated with simulations and an empirical example. Finally, I make recommendations on how researchers should analyze binary treatments. (PsycInfo Database Record (c) 2026 APA, all rights reserved).