distinct (i. e., unchanged by permutations within the X's and Y's separately)
ordered arrangements of these combined sample observations and, moreover, they are
all equally likely. This makes tabulation of the associated null distribution for the SRS
Mann-Whitney statistic relatively straightforward. However, the equally likely nature
of these arrangements does not carry over to the RSS setting, due to the fact that the
ranked set X's and Y's, while still mutually independent, are no longer identically
distributed. For example, even in the case of perfect rankings there is nothing to
prevent the smallest ordered item from one ranked set from being larger than the
largest item from a second ranked set. While this probability will generally be small, it
will not be zero as in the case of SRS. This means that for RSS data it is no longer
sufficient to look at the