Analyze/Stats - Brunner-Munzel test

Analyze/Stats: Brunner-Munzel Test

The Brunner-Munzel test is a nonparametric statistical method used to compare two independent groups and determine whether one tends to yield larger values than the other. Unlike the Mann-Whitney U test, the Brunner-Munzel test does not assume equal variances or identical distribution shapes, making it more robust in situations where these assumptions may not hold.

Why Use This Test?
When Should You Use the Brunner-Munzel Test?
Common Alternatives (when the test isn’t the best fit)
How to Interpret the Results
How the Function is Called
Conclusion

Why Use This Test?

The Brunner-Munzel test is particularly useful when:

Comparing two independent samples that may have unequal variances.
The distributions of the two groups are not assumed to be the same.
Data are ordinal or not normally distributed.
A more robust alternative to the Mann-Whitney U test is desired.

This test assesses whether the probability that a randomly selected observation from one group exceeds a randomly selected observation from the other group is equal to 0.5.

When Should You Use the Brunner-Munzel Test?

You have two independent samples, possibly of different sizes.
The assumption of equal variances between groups is questionable.
You cannot assume that the distributions of the two groups are identical.
You are dealing with ordinal data or data that are not normally distributed.

Common Alternatives (When Brunner-Munzel Isn’t the Best Fit)

How to Interpret the Results

The Brunner-Munzel test provides two key outputs:

Statistic: Measures the difference between the two groups. Larger values indicate greater differences.
p-value: Indicates the probability of observing the data assuming the null hypothesis is true.

This is how you see the Brunner-Munzel results with SimpliStats

Decision Rule:

If p-value < 0.05 (or your chosen significance level): Reject the null hypothesis (there is evidence of a difference between the groups).
If p-value ≥ 0.05: Do not reject the null hypothesis (no statistically significant difference detected).

Example:

Suppose you compare two teaching methods (Group A vs. Group B) and obtain:

W Statistic = 3.14
p-value = 0.002

Since 0.002 < 0.05, you conclude: “There is statistical evidence that the two groups perform differently.“

How the Function is Called

				
					import numpy as np
from scipy.stats import brunnermunzel

# Example data
x = np.array([...])  # Sample from group 1
y = np.array([...])  # Sample from group 2

# Perform the test
statistic, p_value = brunnermunzel(x, y, distribution='t')

Input

x and y: One-dimensional arrays containing the samples.
distribution: Specifies the method to calculate the p-value (‘t’ for t-distribution, ‘normal’ for standard normal distribution).

Output

statistic: The Brunner-Munzel W statistic.
p-value: The associated p-value.

Conclusion

The Brunner-Munzel test is a powerful nonparametric tool for comparing two independent samples, especially when the assumptions of equal variances or identical distributions are not met. Its robustness makes it a preferred choice in many practical situations, offering a more flexible alternative to traditional tests like the Mann-Whitney U.

Home • SimpleStats • User Guide and Documentation