7-year decline in mind when thinking about the magnitude of the effect of playing football. A comparison of football players to all controls is natural, and might be conducted without second thought. Among the controls, however, some played a non-collision sport like baseball or track while others played no sports at all. An investigator might reasonably seek reassurance that this natural comparison has not oversimplified these two version of “not playing football.” At the same time, the investigator does not want to sacrifice power to detect a constant treatment effect in the main comparison en route to obtaining this reassurance by subdividing the data into many slivers of reduced sample size and correcting for multiple comparisons. The method we propose achieves both of these objectives. Our question concerns the effects of high school football. It is important to distinguish this question from questions about the effects of severe head trauma in general. It is at least conceivable that high school football is comparatively harmless, while severe head trauma is not, simply because severe head trauma is not common in high school football, and the benefits of exercise for all football players offset the harm of severe but rare trauma. Conversely, severe head trauma from automotive or other accidents may be difficult to prevent, but if high school football had grave consequences, then it could simply be banned, in the same way that most high schools do not have boxing teams. We ask about the effects of playing football in high school on subsequent cognitive function. The Wisconsin Longitudinal Study describes a specific piece of the US over a specific period of time, and caution is advised about extrapolating its conclusions to other times and places. High School football may have changed since the 1950’s, and the demographic composition of Wisconsin in the 1950’s is not the demographic composition of the US. The Wisconsin Longitudinal Study is primarily a sequence of surveys, and it is impossible to use it to investigate questions not asked in those surveys. For instance, we cannot identify high school students who went on to play professional football, but we suspect they were 6