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Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Discovering Insights with Chi Square Tests: A Hands-on Approach in Python

Aashish
Aashish Last Updated : 26 Feb, 2024
6 min read

Introduction

Let me take you into the universe of chi-square tests and how we can involve them in Python with the scipy library. We’ll be going over the chi-square integrity of the fit test. Whether the reader is just starting or an accomplished information examiner, this guide will outfit you with pragmatic models and experiences so you can unhesitatingly apply chi-square tests in your own work.

Learning objectives

By the end of this article, readers will have:

  • Understood what a Chi-Square Test is and its purpose.
  • Recognized the different types of Chi-Square Tests.
  • Calculated Chi-Square in order to test any relation between two categorical variables.
  • Understand a project implemented in Chi-Square in Python using step-by-step instructions.

This article was published as a part of the Data Science Blogathon.

Table of contents

What is Chi-Square Test?

The Chi-Square test is one of the fact-based interactions used to assess the connection between two all-out factors to figure out the connection between them. This test is extremely straightforward including looking at the noticed frequencies of the factors with their normal frequencies under the supposition that there is no relationship between them. The Chi-Square trial of freedom is usually utilized kind of Chi-Square test. It is applied in circumstances where we have two straight-out factors – like obesity and heart failure event, and we need to research on the off chance that there is an association between them. By doing this we can decide if the example falls into classes in light of our assumptions for the variable dissemination.

Types of Chi-Square Tests

There are several types of Chi-Square Tests, including the chi-square goodness of fit test, the chi-square test of independence, and the chi-square test for homogeneity. The type of test used will depend on the specific research question being addressed and the type of data being analyzed.

Chi-square Goodness of Fit Test: This type of test is used to find out how the observed value of a given condition is significantly (or not) different from the expected value

Chi-square Test of Independence: This type of test is a statistical hypothesis test that can be utilized to determine if 2 categorical and nominal variables are (likely) related or not.

Chi-square Test for Homogeneity: This type of test is used by statisticians to check whether different columns and/or rows of data in a table belong to the same population (or not).

What is a Chi-Square Test? Formula, Examples & Application

Calculating Chi-Square

To calculate the Chi-Square statistic, the observed frequencies are compared to the expected frequencies. The formula for the Chi-Square statistic is:

Chi-Square = Σ((Observed – Expected)^2 / Expected)

Where Observed is the observed frequency for each category and Expected is the expected frequency for each category.

Real World Example

Let me talk through a real-world example of the Chi-Square test to understand how it can help one determine if there’s a relationship between obesity and heart failure rates. As a result, I used a sample of patients diagnosed with heart failure who had their body mass index (BMI) data to categorize them as obese or non-obese.

Now, to calculate the Chi-Square statistic, I created a contingency table showing the number of patients in each category for both obesity (based on BMI) and heart failure variables. After that I’m estimating the expected frequencies for each cell in this table assuming no association between these variables. In the end using the Chi-Square formula I compared the observed and expected frequencies to find if there was any significant association between the two variables.

If my calculated Chi-Square statistic value is greater than the critical value, I reject our null hypothesis that there’s no link between obesity and heart failure. This indicates that obesity is indeed a risk factor for heart failure. Conducting such tests helps us gain valuable insights into relationships within a sample population and develop preventative measures to improve patient outcomes.

Now that we have seen how the process works in theory, let me show you practically, how the calculations and the process works:

Frequency of Heart Failure by Obesity

Chi Square Tests

Our Hypothesis

H0: Obesity and heart failure are independent
HA: Obesity and heart failure are not independent

Frequencies

Chi Square Tests

Here, we calculated the total frequencies by summing up the observed frequencies.

To understand the number of obese patients who would not have undergone heart failure in our sample by chance, we will use the expected values. This is calculated by multiplying each row total by each column total, then dividing the result by the overall sample total. This will give us the expected values of obese patients who did not experience heart failure in our sample population.

Chi Square Tests
Chi Square Tests

Now, let’s calculate the Chi-Square value using the below formula:

Chi-Square = Σ((Observed – Expected)^2 / Expected)

"

And here are the results:

"

Finally, let’s add all the values to find out Chi-Square

Chi-Square = 53.63

Now, we need to determine an alpha level for our test. Let’s set 0.05 as an alpha level and find the critical value of Chi-Square (p). I used the Chi-Square calculator to calculate the p-value.

The p-value is less than .00001 which is, obviously, less than .05 (our alpha value)

Hence, the result is significant. In other words, we reject the null hypothesis which tells us that there is a relationship between Obesity and Heart Failure.

Read more: How to select best split in decision trees using Chi-Square?

Calculating Chi-Square in Python

Now that we did all the fun calculations manually, let’s see if we can do the same using Python. As I previously mentioned, we will be using the scipy package’s chi2_contingency function in Python to do this.

Step 1: Create a Contingency Table

I’m using the crosstab() function from the pandas library. I’m using Heart Failure to group by in the rows and the Obesity variable to group by in the columns. We also need to set margins to true to add row and column subtotals.

heartfailure_crosstab = pd.crosstab(df['obesity'], 
df['heart_failure'], margins=True, margins_name="subtotal")

It returns a contingency table that has this data:

"

Step 2: Compute Chi-Square and p-values

I used the scipy.stats.chi2_contingency function to calculate both my chi-square and p values.

To use this function, I use the following line:

chi, p, dof, expected = chi2_contingency(heartfailure_crosstab)

On a successful run of this above, the function returns the chi-square value to chi, p-value to p, degrees of freedom to dof, and expected values to expected variables respectively.

Step 3: Print P Value

In the above step we stored the output values to variables chi, p, dof, and expected respectively. To find out if p value in this calculation is less than our alpha value (0.05) we use the following command: 

print(p)

The output of the above command will be: 

0.0000000000004257

All I need to do now is to look at the p value and compare it with my alpha to make my conclusion. The above value is less than 0.0001 which is clearly less than 0.05 (our alpha value) and that allows us to conclude that the result is significant. Hence, we reject the null hypothesis which tells us that there is a relation between Obesity and Heart Failures.

Conclusion

The manual calculation of chi-square tests, as you have seen, requires quite a bit of time and manual effort, though Python’s auto calculation using a command is much simpler and more efficient. In this article, I discussed what this test is, different types of chi-square tests, and how to perform a sample chi/square test. Additionally, we learned how to handle similar computations in Python with a single capability by doing so, saving time and effort.

5 Upcoming Python Libraries You Don’t Want to Miss in 2023

The media shown in this article is not owned by Analytics Vidhya and is used at the Author’s discretion.

Frequently Asked Questions

Q1. What is a Chi-Square Test and why is it important in data analysis?

A. A Chi-Square Test is a statistical method used to determine if there is a significant association between categorical variables. It’s crucial in data analysis as it helps identify relationships and patterns within data sets, aiding decision-making and hypothesis testing.

Q2. How do you perform a Chi-Square Test in Python?

A: Performing a Chi-Square Test in Python involves using libraries like scipy and pandas. You can use functions such as scipy.stats.chisquare() or scipy.stats.chi2_contingency() to conduct the test on categorical data, enabling hands-on analysis of relationships and dependencies.

Q3. What are the prerequisites for conducting Chi-Square Tests in Python?

A. Before conducting Chi-Square Tests in Python, one should have a basic understanding of Python programming and familiarity with libraries like pandas and scipy. Additionally, having knowledge of categorical data and the concepts of statistical hypothesis testing would be beneficial for effective utilization.

Q4. How to do Chi Square?


To perform a Chi-Square Test: Define hypotheses, collect categorical data, create a contingency table, calculate expected frequencies, compute the Chi-Square statistic, find critical value, compare, interpret, and repeat if necessary.

blogathoncategorical variableschi square analysisfitGuidelibraryp valuepythonSciPy
Aashish
Aashish

Product Manager with 10+ years of experience in driving product innovation, managing product development and leading agile product teams. Experienced in developing product strategies and executing on tactical plans to ensure successful product launches and profitable product roadmaps. Skilled in developing product roadmaps, managing product portfolios, and creating product requirements.

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What is a Chi-Square Test? Formula, Examples & Application
What is a Chi-Square Test? Formula, Examples & Application
Decoding the Chi-Square Test - Use along with Implementation and Visualization
Decoding the Chi-Square Test - Use along with Implementation and Visualization

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