STEP-UP MULTIPLE TESTING OF PARAMETERS WITH UNEQUALLY CORRELATED ESTIMATES

We consider the problem of simultaneously testing k greater than or eq ual to 2 hypotheses on parameters theta(1), ..., theta(k) using test s tatistics t(1),,..., t,such that a specified familywise error rate alp ha is achieved, Dunnett and Tamhane (1992a) proposed a step-up multipl e test procedure, in which testing starts with the hypothesis correspo nding to the least significant test statistic and proceeds towards the most significant, stopping the first time a significant test result i s obtained (and rejecting the hypotheses corresponding to that and any remaining test statistics). The parameter estimates used in the t sta tistics were assumed to be normally distributed with a common variance , which was a known multiple of an unknown sigma(2), and known correla tions which were equal. In the present article, we show how the proced ure can be extended to include unequally correlated parameter estimate s. Unequal correlations occur, for example, in experiments involving c omparisons among treatment groups with unequal sample sizes. We also c ompare the step-up and step-down multiple testing approaches and discu ss applications;to some biopharmaceutical testing problems.