covariates such that a different set of football players were matched in the matchings using the different versions of control. If the treatment is heterogeneous, say it is modified by some observed covariate that differs between the two versions of control, does “this mean there are two versions of treatment or that there are two groups of individuals that are involved in the two comparisons.” In this setting, the potential for treatment heterogeneity is aliased with the potential for versions of the treatment effect. But does this matter? The logic of § 5.2 is agnostic to why there may be different treatment effects between versions. Thus, I v can be interpreted as assessing how robust our primary analysis is to the existence of versions of treatment or to the existence of effect heterogeneity between the two groups defined by “versions” of control. Figure 2: Comparison of I c (top panel, dark line) and I v (bottom panel, dark line) to Bonferroni corrected (BC) intervals comparing football players vs. “all controls” (top panel, light line), vs. “no sport” controls (bottom panel, top-most light line), and vs. “other sport” controls (bottom panel, bottom-most light line). Notice that I v is very similar in length to the BC interval using “no sport” controls and is noticeably shorter than the BC interval using “other sport” controls. −1 −1/2 0 1/2 1 Constant vs All Controls Versions vs No Sport vs Other Sport Versions Method Bonferroni 20