Home » How to Conduct a Wilcoxon Signed-Rank Test in Python

How to Conduct a Wilcoxon Signed-Rank Test in Python

by Tutor Aspire

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’)

where:

  • 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.

You may also like