What we'd like to do is something similar to the Wilcoxon Signed-Rank estimator.
Observed variables are on a continuous scale.
Measurement scale is at least ordinal. The Wilcoxon based estimator for , under the assumption that the dispersions of the two groups are the same, consists of the median of the differences. That is, suppose that group 1 consists of observations and group 2 consists of To estimate , one might consider looking at , where represents the median. But this results in using only a few of the possible comparisons. One possible extension is to use pairs of combinations to estimate .