# How to Perform Bartlettís Test in Python?

Many statistical tests and procedures presume that the data is normal and has equal variances. These criteria frequently determine whether a researcher can apply a parametric or non-parametric test, frame hypotheses in specific ways, and so on. Bartlett's test is a prominent inferential statistics test that deals with data from a normal distribution. This post will show you how to run Bartlett's test in python.

## What is Bartlett’s test?

Bartlett's test is a statistical test that determines whether or not samples have equal variances. It is a hypothesis test that analyzes the variances of two or more samples to see if they are substantially different from one another.

In the analysis of variance (ANOVA), Bartlett's test is frequently used to check if the variances of the populations from which the samples were drawn are equal. If the variances are equal, the ANOVA test can be performed to compare the sample means. If the variances are not equal, a different statistical test must be employed, such as Welch's ANOVA test.

## Performing Bartlett’s test in Python

The scipy.stats.bartlett function in Python can be used to run Bartlett's test.

### Syntax

stat, p = bartlett(*samples)


Bartlett's test statistic and the p-value are returned by this function after it receives an array of data.

### Parameters

sample 1, sample 2…


Arrays of sample data. Only one-dimensional arrays of any length are permitted.

### Algorithm

• To perform Bartlett's test, the data from each sample is first converted into a set of deviation scores.

• The deviation scores are the differences between each value in the sample and the mean of the sample.

• The variances of the deviation scores for each sample are then calculated and compared using the test statistic.

• If the variances are not significantly different, then the null hypothesis is accepted and the samples are assumed to have equal variances.

• If the variances are significantly different, then the null hypothesis is rejected and the samples are assumed to have unequal variances.

### Example

Using the scipy.stats.bartlett function to run Bartlett's test is demonstrated here −

from scipy.stats import bartlett

# Sample data
data1 = [0.873, 2.817, 0.121, -0.945, -0.055, -1.436, 0.360, -1.478, -1.637, -1.869]
data2 = [-0.208, 0.696, 0.928, -1.148, -0.213, 0.229, 0.137, 0.269, -0.870, -1.204]

# Perform Bartlett's test
stat, p = bartlett(data1, data2)

# Print the test statistic and the p-value
print("Test statistic:", stat)
print("p-value:", p)

# Interpret the results
if p > 0.05:
print("The variances are not significantly different.")
else:
print("The variances are significantly different.")


### Output

Test statistic: 3.663406696073085
p-value: 0.055619798729402634
The variances are not significantly different.


The variances are not significantly different.

In this illustration, Bartlett's test is run on two samples of data using the scipy.stats.bartlett function. The p-value and test statistic are written to the console. Finally, the p-value is used to interpret the data. The variances are not substantially different if the p-value is higher than 0.05. The variances are substantially different if the p-value is less than or equal to 0.05.

## Conclusion

Bartlett's test can be used in machine learning in a variety of situations where it is necessary to compare the variances of two or more samples to determine whether they are significantly different from each other.

In model selection and evaluation, Bartlett's test can be used to compare the variances of the residuals from different models to determine which model has the lowest variance and therefore the best fit for the data. In feature selection, Bartlett's test can be used to compare the variances of different subsets of features to determine which subset of features has the lowest variance and is therefore the most informative for the model.