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J.P. Shaffer 53piece of bad advice I ever had from Walter Shewhart! He told me it was unwiseto put a book out until one was sure that it contained the last word of one’sthinking.”My earlier work in multiple comparisons is described in the interview I gaveto Robinson (2005). Since the time of Tukey’s manuscript, a suggested alternativemeasure of error to be controlled is the False Discovery Rate (FDR),introduced by Benjamini and Hochbert (1995). This is the expected proportionof false rejections, defined as zero if there are no false rejections. ControllingFDR implies that if there are a reasonable number of true rejections a smallproportion of false ones is tolerable. John Tukey himself (personal remark)was enthusiastic about this new approach for some applications.One of my early pieces of work that started a line of research by othersarose from an interest in directional inference. When one tests a hypothesisof the form θ = θ 0 ,whereθ 0 is a specific value, it is usually of interest, ifthe hypothesis is rejected, to decide either that θ>θ 0 or θ