different assumptions, so that one analysis would never be performed if one knew for certain that the assumptions of the other analysis are true. It is a multiple assumptions problem, rather than a multiple hypotheses problem. We discuss the relative merits of the method with respect to more conventional approaches to analyzing multiple comparisons. The method is motivated and illustrated using a study of the possibility that repeated head trauma in high school football causes an increase in risk of early on-set cognitive decline. Keywords: Causal effects, closed testing, full matching, intersection-union test, randomization inference, sensitivity analysis, versions of treatment. Commonly, the effect on an individual caused by a treatment is defined as a comparison of the two potential outcomes that this individual would exhibit under treatment and under control; see Neyman (1923), Welch (1937) and Rubin (1974). Implicit in this definition is the notion that the treatment and control conditions are each well-defined. In particular, it is common to assume that there are “no versions of treatment or control”; see Rubin (1986). By definition, versions of treatment are not intended additions to a study design, but rather potential flaws in the study design. Versions of treatment or control are often associ- ated with finding treatments that occur naturally, rather than experimentally manipulating a tightly controlled, uniform treatment. Versions of one treatment should be distinguished from the intentional study of distinct, competing treatments. When an investigator dis- cusses versions of one treatment, she is expressing a preference for the conception that there is a single treatment, but is acknowledging the possibility that her preferred conception is mistaken. Branded Advil and generic ibuprofen are versions of one treatment — possibly different, but very plausibly expected to be the same — whereas ibuprofen and aspirin 2 1 What are versions of treatment?