the treatment and the treatment exposure of all other individuals. Let be the treatment, the treatment effect for individual is given by . The SUTVA assumption allows us to declare .

One way to look for heterogeneous treatment effects is to divide the study data into subgroups (e.g., men and women, or by state), and see if the average treatment effects are different by subgroup. If the average treatment effects are different, SUTVA is violated. A per-subgroup ATE is called a "conditional average treatment effect" (CATE), i.e. the ATE