In Wu and Chen , multiple comparison procedures with the average for k independent normal means when variances are known or unknown are proposed. The exact critical values are obtained when common variances are known or unknown and sample sizes are all equal. However, when k normal populations are dependent, the problem becomes more complicated. In this article, we consider the multiple comparison procedures with the average for k normal means when populations are not independent by simultaneous confidence interval and subset selection approaches. These procedures have broad applicability in identifying better-than-the-average, worse-than-the-average and not-much-difference-from the average stocks in Dow-Jone industrial stock market and it can also select a subset which includes all better-than-the-average treatments within its own group in experimental design if treatments are not independent. These procedures can be a very useful screening procedure especially when k is large. The comparison of the efficiency between approximation results by Bonferroni inequality and simulation results by Monte Carlo method has been studied and it shows Bonferroni approximates are efficient for equal correlation cases. An example of eight biggest mutual funds in the United States is also given to illustrate the implementation of these multiple comparison procedures with the average.
Journal of Statistics and Management Systems 2(1), pp.73-95