Ideally, a clinical trial should be able to demonstrate not only a statistically significant improvement in the primary efficacy endpoint, but also that the magnitude of the effect is clinically relevant. One proposed approach to address this question is a responder analysis, in which a continuous primary efficacy measure is dichotomized into "responders" and "non-responders." In this paper we discuss various weaknesses with this approach, including a potentially large cost in statistical efficiency, as well as its failure to achieve its main goal. We propose an approach in which the assessments of statistical significance and clinical relevance are separated.