This test is used when we want to compare two means between two paired samples (e.g. before / after) and when the differences between pairs are severely non-normal distributed. The output will display letters “a, A, A+”.
To use this test, open the properties for the column significativity on numeric test. To open these properties, in the general tab of tab definition, right-click in the list of statistical tests and select show cross calculations, then find and right-click column significativity on numeric and select properties. In the properties, click advanced options... and in using, select Wilcoxon’s rank sum test:
Step 1: We calculate the difference between the 2 data sets, for each person i: 
Step 2: Then we rank each absolute 
, excluding the 
.
Step 3: we allocate the sign of each Rank(
), where N is the number of .
Step 4: We calculate the sum of positive Rank (
) and the sum of negative Rank (
). 
.
If 
then there is significative difference between the two means.
Critical Values of ±z
| Level of significance for a Directional Test | ||||
| .05 | .025 | .01 | .005 | .0005 |
| Non-Directional Test | ||||
| -- | .05 | .02 | .01 | .001 |
 |
||||
| 1.645 | 1.960 | 2.326 | 2.576 | 3.291 |
W is compared to a critical value from a reference table.
If 
then there is significative difference between the two means.
Critical Values of ±W for Small Samples:
| Level of significance for a Directional Test | ||||
| .05 | .025 | .01 | .005 | |
| Non-Directional Test | ||||
| N | -- | .05 | .02 | .01 |
| 5 | 15 | -- | -- | -- |
| 6 | 17 | 21 | -- | -- |
| 7 | 22 | 24 | 28 | -- |
| 8 | 26 | 30 | 34 | 36 |
| 9 | 29 | 35 | 39 | 43 |