The documentation team (of which I am a member) recently added more detail to the documentation on the non-parametric multiple comparison tests, but, unfortunately, this will not appear until JMP 13. But to your question, the Steel with Control procedure in JMP does allow unequal treatment sizes. Each pair of treatments is compared by ranking only the observations in the two treatments, calculating the mean rank for each treatment, and then computing the "Score Mean Difference", which is the difference in ranks with a continuity correction applied. The standardized statistic is asymptotically normal. This is based on Hsu (1996). Here are the details of the continuity correction that is applied to the Score Mean Difference: Denote the number of observations in the first treatment by n1 and the number in the second treatment by n2. Rank the observations within the sample consisting of these two treatments. Tied ranks are averaged. Denote the sum of the ranks for the first treatment by ScoreSum1 and for the second treatment by ScoreSum2. If the difference in mean scores is positive, then the Score Mean Difference is given as follows: Score Mean Difference = (ScoreSum1 - 0.5)/n1 - (ScoreSum2 + 0.5)/n2 If the difference in mean scores is negative, then the Score Mean Difference is given as follows: Score Mean Difference = (ScoreSum1 + 0.5)/n1 - (ScoreSum2 -0.5)/n2 I hope this helps answer your question.
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