What we'd like to do is something similar to the Wilcoxon Signed-Rank test. Recall how the sign test and the Wilcoxon Signed-Rank test are different. It will be known as the Rank-Sum test.
Observed variables are on a continuous scale.
Measurement scale is at least ordinal. The last assumption is somewhat the weakest, in the sense that it only needs to be approximately true, in order for the test to have good behavior. A similar normal theory assumption would be that the data are independent, with the first group distributed , and the second group distributed . Then, a test would be constructed to see if , against the possible alternatives. Note that s y 2 is defined in a similar manner.