Wilcoxon Rank Sums:

Wilcoxon rank sums are two statistic s 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.