H$_{τ}$$_{0}$ specifies a particular numerical value τ$_{0}$ for τ and asserts H$_{τ}$$_{0}$ : δ$_{ij}$ = τ$_{0}$ , ∀ i, j , and it is manifested in the observable distribution of Y$_{ij}$ by a within-set shift in the distribution of Y$_{ij}$ by τ$_{0}$ . If H$_{τ}$$_{0}$ were true, then Y$_{ij}$ − τ$_{0}$ Z$_{ij}$ = Y$_{ij}$ (0) would satisfy Fisher’s hypothesis of no effect, H$_{0}$ , and it is commonplace to test H$_{τ}$$_{0}$ by replacing Y$_{ij}$ by Y$_{ij}$ − τ$_{0}$ Z$_{ij}$ and testing H$_{0}$ . Until § 8, we restrict attention to random assignment of treatments within matched sets; however, § 8 considers sensitivity of inferences to departures from this assumption. Of course, people do not decide to play football at random, so § 8 is closer to reality than random assignment. Fisher (1935), Pitman and Welch (1937) used the randomization distribution of the mean difference to test Fisher’s H$_{0}$ , and we follow this approach with the short-tailed delayed word recall scores (DWR), only briefly comparing the mean to a robust M -statistic. The mean is one M -statistic, but not a robust one. Because the matched sets are of unequal sizes, ( m$_{i}$, n$_{i}$ − m$_{i}$ ), we compute the treated-minus-control mean difference in DWR scores within each set i and combine them with efficient weights based on the matched set sizes; see Rosenbaum (2007b, § 4.1) for discussion of these weights, which are implemented in the senfm function of the sensitivityfull package in R with option trim=Inf . As is always true, a 1 − α confidence interval I c for τ is formed by inverting a level- α test, so I c is the shortest interval of values of τ$_{0}$ not rejected by the test; see Lehmann and Romano (2005, § 3) for general discussion. Typically, a two-sided confidence interval is the intersection of two one-sided 1 − α/ 2 confidence intervals; see Shaffer (1974). Ignoring versions of treatment, using the first match in Table 1, and assuming that treatments are randomly assigned within matched sets, we obtain a randomization-based 95% confidence interval of [ − 0 . 308 , 0 . 099] for τ , that is, for a constant effect of playing football on the number of words remembered in the delayed word recall test. Because 10