## Information

**Right tail**, or

**two tails** with positive Z, (W

**-** > μ) , C =

**-**0.5 .

**Left tail**, or

**two tails** with negative Z, (W

**-** < μ) , C = 0.5 .

### Target

Unlike paired t-test that compares the mean of the differences to zero, Wilcoxon Signed-Rank test compares the probability that a random value from Group1 (like before) is greater than his dependent value from Group2 (like after).

When the two distributions have a similar

**shape** you can use the test to compare also the

**median** of the differences to zero.

When the two distributions have a similar

**symmetrical shape**, you can use the test to compare the

**mean** of the differences to zero.

more### Method

**Automatic** - when n

_{1}≤20 and n

_{2}≤20 and the data doesn't have ties, the tool uses the exact value, otherwise the tool uses the z approximation.

**Exact** - when n

_{1}≤20 and n

_{2}≤20 the tool uses the exact value, calculated base on all the possible combinations, otherwise the tool uses the z approximation.

**Z approximation** - the tool uses the z approximations.

**Continuity correction** - relevant only for the Z approximation. It is used since a continuous distribution is used to calculate a discrete distribution.

The page was updated on April 2020 for a full exact distribution (n ≤ 40), instead of a common significant level table.

## R Code

The following R code should produce similar results:

The R code doesn't exclude outliers.