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In multiple comparison procedures often the ordering of populations is of more interest than the testing of hypotheses. In such a situation it is important to control the probability of a Type III error (introduced by Hatter 1957 to indicate that one population is concluded to be better than another when actually it is worse). The studentized differences between means may be used to give ordering conclusions on all pairs of populations under consideration. Although this may be done by setting up confidence intervals using Tukey's honest significant difference, a more efficient method (when the confidence intervals themselves are not of interest) is suggested here, and tables are provided for its implementation. [ABSTRACT FROM AUTHOR]

Let pi[sub I], pi[sub 2] ..... pi[sub k] be k is greater than or equal to 2 sources of observations (treatments, populations) and suppose the "goodness" of treatment pi[sub I] is characterized by the size of an unknown real-valued parameter theta[sub I]. Let theta[sub k] = max[sub 1 less than or equal to I less than or equal to k] theta[sub I] If pi[sub I] is preferred to pi[sub j] when theta[sub I] > theta[sub j], the parameters delta[sub l] = theta[sub [k]] - theta[sub I], I = 1, 2 ..... k reflect in an inverse sense the "goodness" of each treatment relative to the "best" treatment. A general technique for obtaining simultaneous confidence intervals on the delta[sub I] is demonstrated with several examples. This technique can be applied in any setting where comparison-with-control intervals can be computed regarding any pi[sub j] as the control. These results have special importance in ranking and selection problems in that the process of generating upper bounds on the delta[sub I] generates traditional confidence statements of both the indifference zone and the subset selection schools, simultaneously, as established by Hsu (1981). [ABSTRACT FROM AUTHOR]