⎟ distinct (i. e., unchanged by permutations within the X's
and Y's separately) ordered arrangements of the combined sample observations.
Instead we need to calculate the probability of each of the (mk+nq)! permutations
separately and then combine them to obtain the null distribution for URSS. Fortunately
the probabilities of these (mk+nq)! permutations under RSS still do not depend on the
form of the common, continuous F ≡ G under H0, although the tabulation can be
tedious. We illustrate the necessary computations with a small example.
Example 1. For a single X and Y cycle (i.e., m = n = 1) and common X and Y set size k
= q = 2, we must obtain the null probabilities for the 4! = 24 different permutations.
17
Under the assumption of perfect judgement rankings, the RSS observations