When we’d like to test whether or not a single variable is normally distributed, we can create a Q-Q plot to visualize the distribution or we can perform a formal statistical test like an Anderson Darling Test or a Jarque-Bera Test.

However, when we’d like to test whether or not *several *variables are normally distributed as a group we must perform a **multivariate normality test**.

This tutorial explains how to perform the Henze-Zirkler multivariate normality test for a given dataset in Python.

**Related: **If we’d like to identify outliers in a multivariate setting, we can use the Mahalanobis distance.

**Example: Henze-Zirkler Multivariate Normality Test in Python**

The **Henze-Zirkler Multivariate Normality Test **determines whether or not a group of variables follows a multivariate normal distribution. The null and alternative hypotheses for the test are as follows:

H_{0} (null): The variables follow a multivariate normal distribution.

H_{a} (alternative): The variables *do not *follow a multivariate normal distribution.

To perform this test in Python we can use the multivariate_normality() function from the pingouin library.

First, we need to install pingouin:

pip install pingouin

Next, we can import the **multivariate_normality() **function and use it to perform a Multivariate Test for Normality for a given dataset:

#import necessary packages from pingouin import multivariate_normality import pandas as pd import numpy as np #create a dataset with three variables x1, x2, and x3 df = pd.DataFrame({'x1':np.random.normal(size=50), 'x2': np.random.normal(size=50), 'x3': np.random.normal(size=50)}) #perform the Henze-Zirkler Multivariate Normality Test multivariate_normality(df, alpha=.05) HZResults(hz=0.5956866563391165, pval=0.6461804077893423, normal=True)

The results of the test are as follows:

**H-Z Test Statistic:**0.59569**p-value:**0.64618

Since the p-value of the test is not less than our specified alpha value of .05, we fail to reject the null hypothesis. The dataset can be assumed to follow a multivariate normal distribution.

**Related:** Learn how the Henze-Zirkler test is used in real-life medical applications in this research paper.