inferences to Γ = 1 . 25 and Γ = 1 . 5. For Γ = 1 . 25, the intervals are I c = [ − 0 . 534 , 0 . 328] and I v = [ − 0 . 574 , 0 . 464]. For Γ = 1 . 5, the intervals are I c = [ − 0 . 716 , 0 . 517] and I v = [ − 0 . 771 , 0 . 666]. A bias of Γ = 1 . 5 together with two versions of not playing football would be insufficient to mask an effect of one word on the memory test, ± 1. At Γ = 2, not shown in Figure 1, effects of ± 1 word start to be included in the confidence intervals, with I c = [ − 0 . 997 , 0 . 817] and I v = [ − 1 . 082 , 0 . 986]. A bias of Γ = 2 corresponds with an unobserved covariate that triples the odds of playing football and increases the odds of worse memory performance by five-fold. In brief, there is no sign of an effect of high school football on memory scores. Could the absence of any sign of an effect reflect a substantial effect and bias in who plays football? To mask a true effect of ± 1 word, an unobserved bias would have to be moderately large, Γ = 2. Even allowing for both moderate confounding due to unmeasured covariates and versions of treatment, large effects of high school football on memory scores are not consistent with the data. Investigators sometimes candidly report two or more statistical analyses valid under differ- ent assumptions. In the process, they often lose the several advantages of a single, simple, primary analysis, that is, a single analysis with high power against a non-zero constant effect because it uses everyone and avoids needed corrections for multiple testing when several statistical tests are performed. With less candor, investigators sometimes perform several analyses and report some but not all analyses, a perhaps common practice that no one would publicly advocate. Versions of treatment arise in observational studies when treatment or control condi- 9 Discussion: Simultaneous inference about one question under different as- sumptions 22