When do we use it? When there are:

a) Differences between conditions

b) One variable

c) Two conditions

d) Related-design

We will code it like this: D12Ror. The “or” comes from ordinal data and means that Wilcoxon test is non-parametric.

Our dataset would look like the following table. The bolded bits are automatically calculated from the given information.

 Participants Condition 1 Condition 2 Difference between conditions 1 10 6 4 2 5 2 3 3 4 2 2 4 5 2 3 Total scores 24 12 Mean scores

In some cases, we might have negative values in the Difference column, when it comes to computing ranks of the Differences, we ignore the signs. See below for an example.

 Participants Condition 1 Condition 2 Differences Ranks of Differences 1 1 4 -3 1 2 3 8 -5 2.5 3 5 10 -5 2.5

The Ranks of Differences ranks the values of the Difference column. It starts by assigning 1 to the lowest value (-3) and then we have two 5s in second and third position. So we calculate their tied ranks: 2+3=5/2=2.5 and assign it to them.

Note: when the Difference column has a zero value (i.e. some participant scored equally in both conditions), the ranking cannot be computed. In that case, we assign the label “tie” inside the row and we continue our ranking (i.e. if the 3rd rank turned out to be tie, we placed a tie label in the appropriate row and assign the third rank to the next candidate.)

The next post: Wilcoxon test – Practice Data will go through an example.