Enumerating anything but small permutation distributions is unmanagable, so instead we take a random sample of the permutations
Ranks and the Wilcoxon Rank-Sum test
Given a sample X1, X2, ..., XN, of N observations, the rank of Xi among the N observations is denoted by R(Xi), and is given by:
R(Xi) = number of Xj's <= Xi
Let W be the sum of the ranks from one treatment group. The Wilcoxon rank-sum test is a two-sample permutation test based on W.
Revisiting our earlier example:
|New group||Old group||New group ranks||Old group ranks||New group rank sum|
Let's examine the permutation distribution of the new group rank sums:.
Steps in the Wilcoxon rank-sum test, Tables, adjustment for ties.