Mann-Whitney U Test | Fera Analytics

Introduction

The Mann-Whitney U test, also known as the Wilcoxon rank-sum test, is a non-parametric statistical test used to determine if there is a significant difference between the distributions of two independent groups. This lesson explores the concept of the Mann-Whitney U test, its assumptions, practical applications, and implementation in Python.

What is the Mann-Whitney U Test?

The Mann-Whitney U test compares the medians of two independent samples to determine if they likely come from the same population. It is particularly useful when the assumptions of parametric tests like the t-test (e.g., normality of data) are not met or when analyzing ordinal or non-normally distributed data.

Assumptions of the Mann-Whitney U Test

The Mann-Whitney U test does not assume that the data are normally distributed. However, it does assume:

The observations within each group are independent.
The measurements are at least ordinal, meaning the data can be ranked.

Performing the Mann-Whitney U Test in Python

Using scipy.stats

Scipy library provides functions to perform the Mann-Whitney U test in Python. Here’s an example of conducting a Mann-Whitney U test:

import numpy as np
from scipy.stats import mannwhitneyu

# Example data (two independent groups)
group1_scores = np.array([85, 92, 88, 78, 90])
group2_scores = np.array([79, 83, 77, 81, 85])

# Mann-Whitney U test
statistic, p_value = mannwhitneyu(group1_scores, group2_scores)

# Interpret results
alpha = 0.05  # significance level
if p_value < alpha:
    print("Reject null hypothesis: There is a significant difference between the groups.")
else:
    print("Fail to reject null hypothesis: There is no significant difference between the groups.")

Practical Applications

The Mann-Whitney U test is applied in various fields, including:

Medicine: Comparing treatment outcomes between patient groups.
Education: Analyzing test scores between different teaching methods.
Business: Evaluating performance metrics across different departments.
Social Sciences: Studying differences in survey responses across demographic groups.

Conclusion

The Mann-Whitney U test provides a robust method for comparing distributions of two independent groups when parametric assumptions are not met. By understanding its principles, assumptions, and how to implement it in Python, researchers and analysts can effectively analyze non-parametric data, draw valid conclusions, and make informed decisions based on statistical evidence.