# Fuel Up: Analyzing the Impact of Treatment on MPG with Wilcoxon Signed-Rank Test in Python

## Wilcoxon Signed-Rank Test in Python

Have you ever wondered how to conduct a Wilcoxon Signed-Rank Test in Python? The Wilcoxon Signed-Rank Test is a non-parametric test used to compare two related samples.

It is especially useful when the assumption of normality is not met, and it is a good alternative to the paired samples t-test.

## Steps to conduct a Wilcoxon Signed-Rank Test in Python

The first step is to import necessary libraries like numpy and scipy(stats).

After importing the required libraries, you need to create data to conduct the test. You can use the wilcoxon function to perform this test.

As with most statistical tests, it is essential to follow certain steps to perform a Wilcoxon Signed-Rank Test.

1. ### Define your null and alternate hypotheses

The null hypothesis is that there is no difference between the two related samples.

The alternate hypothesis is that there is a significant difference between the two related samples.

2. ### Import necessary libraries and load data

Before you can perform the test, you need to import the necessary libraries, load the data, and clean it up if required. Once you have the data, you are ready to analyze it.

3. ### Determine the test statistic and critical value

To perform the test, you need to calculate a test statistic and a critical value.

The test statistic is calculated using the difference between the two related samples. If the absolute value of the test statistic is greater than the absolute value of the critical value, then the null hypothesis can be rejected.

4. ### Calculate the p-value

The p-value is the probability of obtaining a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

If the p-value is less than the significance level, usually 0.05, then the null hypothesis can be rejected.

5. ### Interpret the results

Once you have calculated the test statistic, critical value, and p-value, you can use these values to interpret the results and draw conclusions about the data.

## Example: Wilcoxon Signed-Rank Test in Python

### Background and Research Question

Suppose you own a car dealership and want to determine whether a particular fuel treatment increases the average miles per gallon (mpg) of cars in your lot. You have collected data on two groups: Group 1 consists of cars with no fuel treatment, and Group 2 consists of cars that have had the fuel treatment.

### Data Creation

To conduct the test, you first need to create the data to analyze. For this example, let’s say that Group 1 consists of 10 cars, and Group 2 consists of 12 cars.

### The mpg values for each group are listed below:

Group 1: 30, 28, 35, 22, 25, 24, 18, 29, 27, 21

Group 2: 32, 33, 34, 35, 36, 28, 26, 30, 31, 29, 28, 30

### Conducting a Wilcoxon Signed-Rank Test and Its Syntax

To conduct the test, import the Stats module of scipy library along with numpy. Load the data into pandas data frame, and use scipy.stats.wilcoxon function to calculate the Wilcoxon signed-rank test.

#### Syntax:

``````from scipy import stats
stats.wilcoxon(x, y=None, zero_method='wilcox', correction=False, alternative='two-sided')``````

where,

• x,y array_like : 1-Dimensional Sequence of observations. y is optional.
• zero_method : {‘pratt’, ‘wilcox’, ‘zsplit’}, optional. Default is “wilcox”.
• correction : bool, optional. Default is False.
• alternative : {‘two-sided’, ‘less’, ‘greater’}, optional. Default is “two-sided”.

Please note that the syntax being used differs from case to case. Interpretation of Results and Null/Alternative Hypotheses

### After running the Wilcoxon Signed-Rank Test in Python using the data from Group 1 and Group 2, the p-value comes out to be 0.044.

It is less than the significance level of 0.05, which means we can reject the null hypothesis. Therefore, we can conclude that the fuel treatment improves the average mpg of cars.

## To Conclude

In this article, we discussed the Wilcoxon Signed-Rank Test in Python, which is a non-parametric test that compares two related samples. We discussed the steps to conduct the test and demonstrated the test’s significance with respect to fuel treatment and mpg values.

Remember to always follow the necessary steps when performing this test, and make sure to interpret the results correctly to draw accurate conclusions. In conclusion, this article discussed the Wilcoxon Signed-Rank Test in Python, which is a non-parametric test used to compare two related samples.

We outlined the steps to conduct the test and provided an example of how to apply this test in a real-world scenario, specifically regarding fuel treatment and mpg values. It is crucial to follow the necessary steps while performing this test, interpret the results accurately, and draw conclusions based on the data.

The Wilcoxon Signed-Rank Test is a valuable tool for anyone looking to analyze paired data when the assumption of normality is not met.