Statistical Inference for the Difference Between the Best Treatment Mean and a Control Mean

• Published in: Journal of the American Statistical Association Vol. 101; no. 475; pp. 1050 - 1058
• Main Authors: Lee, Chu-In Charles, Peng, Jianan, Liu, Lin
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01-09-2006; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Confidence intervals; Critical values; Dunnett's procedure; Exact sciences and technology; General topics; Gupta's subset selection; Integers; Interval estimators; Isotonic regression; Kuhn-Tucker equivalence theorem; Linear algebra; Lower confidence bound; Mathematics; Null hypothesis; Optimal solutions; P values; Parametric inference; Prior learning; Probability and statistics; Ratio test; Regression analysis; Sciences and techniques of general use; Sociological methodology; Statistical inference; Statistical methods; Statistical theories; Statistics; Theory and Methods; Lower bound; Optimization method; Dunnett's procedure; Linear programming; Kuhn-Tucker equivalence theorem; Statistical estimation; Algorithm; Mean estimation; Lower confidence bound; Constrained optimization; Statistical method; Linear constraint; Isotonic regression; Gupta's subset selection; Inequality constraint; Application; Subset selection
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214506000000258

In many experiments, researchers are interested in comparing several treatment means with a control mean. When there are some treatments significantly better than the control, it is often of interest to evaluate the difference between the best treatment mean and the control mean and to identify the best treatment. In this article we derive lower confidence bounds for the aforementioned difference for the case that treatments are at least as effective as the control and for the case that no restriction is placed on the treatment means and the control mean. The evaluation of the lower confidence bound for the difference between the best treatment mean and the control mean is a concave programming problem subject to homogeneous linear inequality constraints. We propose two efficient computation algorithms and discuss the connection between our procedures and Gupta's subset selection procedure. We compare the expected lower confidence bounds of the two procedures with that of Dunnett's procedure. An application to a real-life data is included.