Two-sided Confidence Bands with the Inferential Sensitivity of One-Sided Bands

In this article, we consider investigating whether any of k treatments are better than a control under the assumption of each treatment mean being no less than the control mean. A classic problem is to find the simultaneous confidence bounds for the difference between each treatment and the control. Compared with hypothesis testing, confidence bounds have the attractive advantage of telling more information about the effective treatment. Generally, the one-sided lower bounds are provided as it's enough for detecting effective treatment and the one-sided lower bounds has sharper lower bands than two-sided ones. However, a two-sided procedure provides both upper and lower bounds on the differences. In this article, we develop a new procedure which combines the good aspects of both the one-sided and the two-sided procedures. This new procedure has the same inferential sensitivity of the one-sided procedure proposed by Zhao (2007 Zhao , H. B. ( 2007 ). Comparing several treatments with a control . J. Statist. Plann. Infer. 137 : 2996 – 3006 .Crossref], Web of Science ®] , Google Scholar]) while also providing simultaneous two-sided bounds for the differences between treatments and the control. By our computation results, we find the new procedure is better than Hayter, Miwa and Liu's procedure (Hayter et al., 2000 Hayter , A. J. , Miwa , T. , Liu , W. ( 2000 ). Combining the advantages of one-sided and two-sided procedures for comparing several treatments with a control . J. Statist. Plann. Infer. 86 : 81 – 99 .Crossref], Web of Science ®] , Google Scholar]), when the sample size is balanced. We also illustrate the new procedure by an example.