Multiple Comparisons and Type III Errors

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 Harter 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.