Understanding and Using the Wilcoxon Test in Python

Wilcoxon test, also known as the Wilcoxon rank-sum test or the Mann-Whitney test, is a non-parametric statistical test used to compare the medians of two groups. It is often used as an alternative to the t-test when the assumptions of normality or equal variances are not met. In this tutorial, we will learn how to perform a Wilcoxon test in Python using the scipy library.

Installing the Required Libraries

Before we can start, we need to make sure that we have the necessary libraries installed. We will be using the scipy library, which can be installed using pip. Open up your terminal or command prompt and run the following command:

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pip install scipy

Preparing the Data

To perform the Wilcoxon test, we need to have two sets of data that we want to compare. Let’s say we have the following data for two groups, group A and group B:

Group A: [1, 3, 5, 7, 9]

Group B: [2, 4, 6, 8, 10]

We can store this data in Python as follows:

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group_a = [1, 3, 5, 7, 9]
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group_b = [2, 4, 6, 8, 10]

Performing the Wilcoxon Test

Now that we have our data, we can perform the Wilcoxon test using the scipy.stats.mannwhitneyu function. This function takes in the two groups of data as arguments and returns the statistic and the p-value.

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from scipy.stats import mannwhitneyu
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statistic, p_value = mannwhitneyu(group_a, group_b)
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print("Statistic:", statistic)
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print("p-value:", p_value)

The output of this code will be:

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Statistic: 10.0
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p-value: 0.6904761904761905

The p-value tells us the probability of obtaining a result as extreme as the one we got, given that the null hypothesis is true. In this case, the null hypothesis is that the two groups are drawn from the same population. If the p-value is less than a predetermined threshold (usually 0.05), we can reject the null hypothesis and conclude that the two groups are significantly different.

Conclusion

In this tutorial, we learned how to perform a Wilcoxon test in Python using the scipy library. We imported the mannwhitneyu function and used it to calculate the statistic and p-value for two groups of data. We also learned how to interpret the p-value and use it to make statistical inferences about the data.

I hope this tutorial was helpful! If you have any questions or suggestions, please don’t hesitate to leave a comment.

References:

Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50–60.

Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83.