Mann-Whitney U Test Examples for Beginners

Explore practical examples of the Mann-Whitney U Test, a powerful non-parametric statistical tool.
By Jamie

Understanding the Mann-Whitney U Test

The Mann-Whitney U Test is a non-parametric statistical test used to determine whether there is a difference between the distributions of two independent samples. Unlike parametric tests, it does not assume that the data follows a specific distribution, making it suitable for data that is ordinal or not normally distributed. This test is particularly useful in various fields such as medicine, psychology, and market research. Below are three practical examples of the Mann-Whitney U Test in action.

Example 1: Comparing Test Scores of Two Teaching Methods

In an educational study, researchers want to evaluate the effectiveness of two different teaching methods on students’ performance. Method A is a traditional lecture-based approach, while Method B incorporates interactive group activities. The researchers collect test scores from two independent groups of students:

  • Group 1 (Method A): 78, 85, 90, 92, 88
  • Group 2 (Method B): 82, 87, 95, 91, 94

To assess whether there is a significant difference in the test scores between the two groups, the Mann-Whitney U Test is applied. The null hypothesis states that there is no difference in the distributions of the test scores from the two methods. After performing the test, the results indicate a U statistic of 7, with a p-value of 0.03. Since the p-value is less than the significance level of 0.05, the researchers reject the null hypothesis, concluding that there is a statistically significant difference in the effectiveness of the two teaching methods.

Notes: This example illustrates how educational researchers can utilize the Mann-Whitney U Test to compare the performance of different teaching strategies without assuming normal distribution of scores.

Example 2: Analyzing Customer Satisfaction Ratings

In a market research study, a company wants to compare customer satisfaction ratings for two different products. The satisfaction ratings are collected on a scale from 1 to 10, where 1 indicates very dissatisfied and 10 indicates very satisfied. The ratings from customers using Product X and Product Y are as follows:

  • Product X: 7, 8, 6, 9, 5
  • Product Y: 8, 9, 10, 7, 6

The Mann-Whitney U Test is employed to test the null hypothesis, which states that there is no difference in customer satisfaction ratings between the two products. The analysis yields a U statistic of 10, with a p-value of 0.15. Since this p-value is greater than 0.05, the null hypothesis cannot be rejected, indicating that there is no significant difference in customer satisfaction ratings between Product X and Product Y.

Notes: This example demonstrates how the Mann-Whitney U Test can be effectively used in market research to gauge customer satisfaction without requiring normally distributed data.

Example 3: Evaluating Pain Levels After Two Treatments

In a clinical trial, researchers aim to compare the pain levels reported by patients after receiving two different pain management treatments: Treatment A (medication) and Treatment B (physical therapy). Pain levels are measured on a scale from 0 (no pain) to 10 (worst pain). The reported pain levels are:

  • Treatment A: 3, 5, 4, 2, 6
  • Treatment B: 4, 3, 5, 1, 2

The Mann-Whitney U Test is performed to investigate whether there is a significant difference in pain levels between the two treatments. The null hypothesis posits that there is no difference in pain levels after the two treatments. The test results show a U statistic of 8, with a p-value of 0.04. Given that the p-value is less than the significance level of 0.05, the null hypothesis is rejected, suggesting that there is a significant difference in pain levels between the two treatments.

Notes: This clinical example highlights the practical application of the Mann-Whitney U Test in healthcare research, where data may not meet the assumptions of parametric tests.