The Wilcoxon Signed-Rank Test is the non-parametric version of the paired samples t-test.
It is used to test whether or not there is a significant difference between two population means when the distribution of the differences between the two samples cannot be assumed to be normal.
This tutorial explains how to conduct a Wilcoxon Signed-Rank Test in Python.
Example: Wilcoxon Signed-Rank Test in Python
Researchers want to know if a new fuel treatment leads to a change in the average mpg of a certain car. To test this, they measure the mpg of 12 cars with and without the fuel treatment.
Use the following steps to perform a Wilcoxon Signed-Rank Test in Python to determine if there is a difference in the mean mpg between the two groups.
Step 1: Create the data.
First, we’ll create two arrays to hold the mpg values for each group of cars:
group1 = [20, 23, 21, 25, 18, 17, 18, 24, 20, 24, 23, 19] group2 = [24, 25, 21, 22, 23, 18, 17, 28, 24, 27, 21, 23]
Step 2: Conduct a Wilcoxon Signed-Rank Test.
Next, we’ll use the wilcoxon() function from the scipy.stats library to conduct a Wilcoxon Signed-Rank Test, which uses the following syntax:
wilcoxon(x, y, alternative=’two-sided’)
- x: an array of sample observations from group 1
- y: an array of sample observations from group 2
- alternative: defines the alternative hypothesis. Default is ‘two-sided’ but other options include ‘less’ and ‘greater.’
Here’s how to use this function in our specific example:
import scipy.stats as stats #perform the Wilcoxon-Signed Rank Test stats.wilcoxon(group1, group2) (statistic=10.5, pvalue=0.044)
The test statistic is 10.5 and the corresponding two-sided p-value is 0.044.
Step 3: Interpret the results.
In this example, the Wilcoxon Signed-Rank Test uses the following null and alternative hypotheses:
H0: The mpg is equal between the two groups
HA: The mpg is not equal between the two groups
Since the p-value (0.044) is less than 0.05, we reject the null hypothesis. We have sufficient evidence to say that the true mean mpg is not equal between the two groups.