Chi-square Test

Performing the Chi-square Test in Python: Step-by-Step Implementation


Are you interested in analyzing categorical data to determine if there is a significant association between variables? Look no further than the Chi-square test! In this beginner’s guide, we will walk you through the fundamentals of the Chi-square test and show you how to perform it in Python from scratch. So, let’s dive in and unlock the power of statistical analysis with the Chi-square test!

Understanding Chi-square Test

The Chi-square test is a statistical hypothesis test used to determine if there is a significant association between two categorical variables. It helps us understand whether the observed frequencies in our data differ significantly from the expected frequencies under a null hypothesis of independence.

Assumptions of Chi-square Test

Before diving into the implementation, let’s discuss the assumptions associated with the Chi-square test. It is essential to ensure that these assumptions hold true for the validity of the test. The main assumptions are:

  1. Independence: The observations are independent of each other.
  2. Sample Size: The sample size is sufficiently large.
  3. Expected Frequency: The expected frequency for each cell is at least 5.

Types of Chi-square Tests

There are several variations of the Chi-square test, each suited for different scenarios. Let’s explore some common types of Chi-square tests:

1. Pearson’s Chi-square Test

Pearson’s Chi-square test is used to analyze the association between two categorical variables when the observed frequencies are independent. It compares the observed frequencies to the expected frequencies.

2. Yates’ Correction for Continuity

Yates’ correction for continuity is a modification of Pearson’s Chi-square test. It is used when analyzing 2×2 contingency tables to account for potential bias caused by small sample sizes.

3. Fisher’s Exact Test

Fisher’s exact test is used when the sample size is small, and the assumptions of Pearson’s Chi-square test are not met. It provides an exact p-value rather than an approximate one.

4. Likelihood Ratio Test

The likelihood ratio test is an alternative to Pearson’s Chi-square test when the expected frequencies are not fixed. It considers the likelihood of different models to determine the best fit.

Chi-square Test in Python

Now that we have a solid understanding of the Chi-square test, let’s explore how to implement it in Python. Follow the steps below:

Step 1: Importing Required Libraries

To perform the Chi-square test, we need to import the necessary libraries, such as numpy and scipy.stats.

pythonCopy codeimport numpy as np
from scipy.stats import chi2_contingency

Step 2: Data Preparation

Prepare your data in the form of a contingency table, where rows represent one variable, and columns represent another variable. Ensure that the data is categorical.

Step 3: Calculating Observed and Expected Frequencies

Using the contingency table, calculate the observed frequencies and expected frequencies using the chi2_contingency() function from the scipy.stats module. This function returns the chi-square statistic, p-value, degrees of freedom, and the expected frequencies.

pythonCopy codeobserved_freq = np.array([[a, b], [c, d]])  # Replace with your actual data
chi2, p_val, dof, expected_freq = chi2_contingency(observed_freq)

Step 4: Performing Chi-square Test

With the observed and expected frequencies calculated, we can now perform the Chi-square test using the obtained values. This test will assess whether there is a significant association between the categorical variables.

Interpreting the Chi-square Test Results

Once the Chi-square test is performed, it is crucial to interpret the results correctly. The p-value obtained from the test indicates the probability of observing the association between variables if they were independent. If the p-value is below a predefined significance level (e.g., 0.05), we reject the null hypothesis of independence and conclude that there is a significant association between the variables.

Visualizing Chi-square Test Results

Visualizing the results of the Chi-square test can provide a clearer understanding of the association between variables. You can use various visualization techniques such as bar plots, stacked bar plots, or heatmaps to represent the observed and expected frequencies.

Advantages and Limitations of Chi-square Test

The Chi-square test offers several advantages, including its simplicity, ability to handle categorical data, and versatility across different scenarios. However, it also has certain limitations. For instance, it assumes independence, requires an adequate sample size, and is not suitable for analyzing continuous variables.

Real-World Applications of Chi-square Test

The Chi-square test finds applications in various fields such as healthcare, market research, social sciences, and biology. It can be used to analyze survey responses, examine the effectiveness of treatments, assess the impact of marketing campaigns, and investigate genetic associations.


In conclusion, the Chi-square test is a powerful statistical tool for analyzing categorical data and determining associations between variables. By following the steps outlined in this guide, you can implement the Chi-square test in Python from scratch. Remember to interpret the results carefully and visualize the findings to gain deeper insights into your data.