*48*

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, weâ€™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, weâ€™ll use theÂ wilcoxon() functionÂ from the scipy.stats library to conduct a Wilcoxon Signed-Rank Test, which uses the following syntax:

**wilcoxon(x, y, alternative=â€™two-sidedâ€™)**

where:

**x:Â**an array of sample observations from group 1**y:Â**an array of sample observations from group 2**alternative:Â**defines the alternative hypothesis. Default is â€˜two-sidedâ€™ but other options include â€˜lessâ€™ and â€˜greater.â€™

Hereâ€™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 isÂ **10.5Â **and the corresponding two-sided p-value isÂ **0.044**.

**Step 3: Interpret the results.**

In this example, the Wilcoxon Signed-Rank Test uses the following null and alternative hypotheses:

**H _{0}:Â **The mpg is equal between the two groups

**H _{A}:Â **The mpg isÂ

*notÂ*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.