Wilcoxon Rank Sums

Wilcoxon rank sums are two statistics T⁺ and T^– computed from paired replicates data.

Suppose we have two sets of pairs of measurements (x_i,y_i), i=1,…,N for each of N experimental units. We compute differences

and their absolute values:

Then we replace D_i by ranks and split the values d_i into two groups according to the sign of corresponding d_i. The sums of ranks for positive and negative differences are named Wilcoxon rank sums T⁺ and T^–, respectively.

Wilcoxon rank sums are used to compute the test statistic for the Wilcoxon signed ranks test