Adaptive clinical trials can use interim data to select the treatment, patient population, or endpoint for final testing. Existing methods generally control family-wise type I error marginally, averaging over the selections that the trial might have made. However, in the drug development and regulatory process, the ultimate decision generally concerns the adaptively selected hypothesis, raising an important question: conditional on a hypothesis being selected, how often is it incorrectly rejected? Marginal error is a weighted average of these selection-conditional error rates, and therefore marginal error control does not imply selection-conditional error control. We formalize this distinction and study a two-stage adaptive trial in which either one or two of five treatments continue after interim selection. A commonly used closed combination test controls marginal family-wise error, but in our one-treatment illustration each zero-effect treatment has selection-conditional error of roughly 9.4% at nominal 5%. In contrast, a selective Gaussian test and a stage-2-only test control selection-conditional family-wise error in both illustrations. Perhaps surprisingly, the selective Gaussian test is also more powerful than the combination test in these examples. We call for more discussion in the clinical-trial community about the appropriate statistical error criterion for adaptive confirmatory claims.