The problem of selecting the one best treatment from among several ones has been long studied. However, this type of statistical procedure has little chance of being used in practice. This is due to some serious deficiencies in the statistical modeling, rendering them unsuitable for application. The purpose of this research is to overcome as much as possible the deficiencies of earlier procedures. The principal investigator plans to develop a new statistical decision procedure for simultaneously selecting and estimating the best treatment with a preliminary test, which allows a significant test of the null hypothesis and an interval estimate together with the selection rule simultaneously. A general formulation and a decision procedure are considered for location and scale parameter families of distributions such as exponential, gamma, lognormal, normal and other distributions. An extension of the decision procedure to the repeated measurements design will be carefully studied because this type of design is often used in many applied fields, especially in medical research on treatment comparisons. Dependence and heteroscedasticity of the response variables will be allowed for and hence a multivariate approach and two-stage, sequential sampling procedure will be investigated. In addition to selection of a best one, the investigator also plans to develop an alternate selection procedure which allows the experimenters to include all possible best treatments in his subset when there has more than one best in medical trials where side effects become important and to leave the final judgement to the decision maker. The new subset selection procedure is able to be used with a reasonable probability confidence for any fixed but arbitrary sample size. This, and the fact that it does not require a least difference between the best and the next best treatments, form a large part of its attraction to experimenters. Decision rules shall be developed for models including normal, gamma, exponential, binomial, and other continuous and discrete distributions. Properties and optimality of the new selection rule will also be studied. A modified selection procedure with inference concerning the best is also proposed, which is more realistic in certain medical experiments. Comparison of the proposed procedures with existing selection and multiple decision procedures is the last objective of the research.
