Wilcoxon Signed-Rank test

Two dependent samples, non-parametric paired test
Video Informations Paired T-test
The test compares the probability to get higher value from group1 with the probability to get higher value from dependent group2.

Test calculation

Enter raw data directly
Enter raw data from excel

Enter sample data

Header: You may change groups' name to the real names.
Data: When entering data, press Enter, , or Space after each value.
Difference: Difference = Right column - Left column.

The tool ignores empty cells or non-numeric cells.

Enter sample data

You may copy data from Excel, Google sheets or any tool that separate data with Tab and Line Feed.
Copy the data, one block of 3 consecutive columns includes the header, and paste below.
Copy the data,
example from excel

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

Results

Skewness Shape:


The difference between the expected SD and the sample SD

validation message

Information

Hypotheses
H0: Before = After
H1: Before < > After
Test statistic
z statistic
Normal distribution
z distribution left tailed z distribution two tailed z distribution right tailed
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 n1≤20 and n2≤20 and the data doesn't have ties, the tool uses the exact value, otherwise the tool uses the z approximation.
Exact - when n1≤20 and n2≤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.