WILCOXON SIGNED-RANKS TEST

The Wilcoxon test compares the distribution groups. The groups are related in one of two ways:

1. The same objects/people have been tested under two different conditions.

2. Pairs of objects/people have been matched on the same basis before being tested.

The purpose of this test is to determine whether the differences between the groups favor one group over the other. The sign test, which you have just read about, concerns itself with only the direction of the differences between the pairs; it does not consider the size of the differences. All we recorded by using a plus or a minus sign for each matched pair of scores for the sign test was whether one of the pairs was larger or smaller; we did not record how large or small this difference was. The sign test does not use all the information that is available. However, the Wilcoxon test concerns itself not only with the direction of the differences but also with their size . It makes a distinction between these differences by ranking them. The critical value for this test can be found on a table for this particular test. The requirements of the Wilcoxon signed-ranks test are as follows :

1. Ordinal data

2. Two groups

3. Related groups

4. Ranked data

The symbols used for this test are: N = number of matched pairs, excluding those with a deviation (D) of zero; T = the smaller value for either & pound ; R ⁺ or R ^- .