Decoding the Chi-Square Test - Use along with Implementation and Visualization

In the last blog we looked at a test to find out correlation between the continuous variable in our data which you can read here. In this blog we will take a look at an important test that we can conduct to find out the correlation between the categorical variables in our data is Chi-Square Test, I will try to make the blog easy to understand focusing more on the implementation rather than the theory behind the test in this blog we will be looking at topics like:

1. What is Chi-Square Test?
2. How to implement the Chi-Square Test in Python?
3. How to visualize the results of the test using a heat-map?

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

What is Chi-Square Test?

Chi-Square test is a statistical test which is used to find out the difference between the observed and the expected data we can also use this test to find the correlation between categorical variables in our data. The purpose of this test is to determine if the difference between 2 categorical variables is due to chance, or if it is due to a relationship between them.

It is important to note that the variables to be compared should have only 2 categories i.e 1 and 0 the chi-square test fails to determine the correlation between variables with more than 2 categories.

While conducting the chi-square test we have to initially consider 2 hypothesis i.e the Null Hypothesis and the Alternate Hypothesis.

1. H0 (Null Hypothesis) = The 2 variables to be compared are independent.
2. H1 (Alternate Hypothesis) = The 2 variables are dependent.

Now, if the p-value obtained after conducting the test is less than 0.05 we reject the Null hypothesis and accept the Alternate hypothesis and if the p-value is greater that 0.05 we accept the Null hypothesis and reject the Alternate hypothesis. Now, let’s move onto the implementation. If you want to know more about the theory behind the Chi-square test you can check this out.

How to implement the Chi-Square Test in Python?

To implement the chi-square test in python the easiest way is using the chi2 function in the sklearn.feature_selection. The function takes in 2 parameters which are:

1.  x (array of size = (n_samples, n_features))
2.  y (array of size = (n_samples)) the y parameter is referred to as the target variable.

The function returns 2 arrays containing the chi2 statistics and p_values.

We will be using the p_values to determine the dependency of the variables. In the example below, I use a sample dataset with three columns: Gender, Smoking, and Drinking. I initialized the values of these columns randomly. The dataset can be found on my Github repository here. Now we will set our null hypothesis to state that the variables we compare are independent, while our alternative hypothesis will assert that the variables are dependent.

from sklearn.feature_selection import chi2
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# Load Dataset
df = pd.read_csv('SampleData.csv')

# Create a DataFrame where the column names and index are the same
# This matrix resembles the correlation matrix obtained from df.corr()
# Initialize the values in this matrix with 0
resultant = pd.DataFrame(data=[(0 for i in range(len(df.columns))) 
for i in range(len(df.columns))], columns=list(df.columns))
resultant.set_index(pd.Index(list(df.columns)), inplace=True)

# Find p-values for all columns and populate the resultant matrix
for i in list(df.columns):
    for j in list(df.columns):
        if i != j:
            chi2_val, p_val = chi2(np.array(df[i]).reshape(-1, 1), np.array(df[j]).reshape(-1, 1))
            resultant.loc[i, j] = p_val

print(resultant)

from sklearn.feature_selection import chi2
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# Load the dataset
df = pd.read_csv('SampleData.csv')

# Create a DataFrame where the column names and index are the same
# This matrix resembles the correlation matrix obtained from df.corr()
# Initialize all values in this matrix to 0
resultant = pd.DataFrame(data=np.zeros((len(df.columns), len(df.columns))), columns=list(df.columns))
resultant.set_index(pd.Index(list(df.columns)), inplace=True)

# Calculate p-values for all column pairs and populate the resultant matrix
for i in list(df.columns):
    for j in list(df.columns):
        if i != j:
            chi2_val, p_val = chi2(np.array(df[i]).reshape(-1, 1), np.array(df[j]).reshape(-1, 1))
            resultant.loc[i, j] = p_val

# Print the resultant DataFrame containing p-values
print(resultant)

In the above code, you can see that the p-values between the same columns are not calculated (Line 21). This omission occurs because we know that the correlation between the same columns will be very high, resulting in a value very close to 0. The code above will print a data frame that will look like the image below. Now that we have the results we will move onto visualizing the data frame.

How to visualize the results of the test using a heat-map?

Now that we have the data-frame will use the Heat map to plot the graph similar to the heat map used for visualising Pearson correlation. For this we will use the seaborn library. The code for visualization is as shown below-# Plotting a heatmap fig = plt.figure(figsize=(6,6)) sns.heatmap(resultant, annot=True, cmap=’Blues’) plt.title(‘Chi-Square Test Results’) plt.show()

The result produced by the above code will be as represented in the figure below now, using this heat map we can easily interpret the outcome of the test.

Observations

1. It can be seen that the diagonal has values equal to 0 as we had discussed above.
2. We also observe that the Gender and Drinking columns have a high correlation, as their value is less than 0.05 and tends to be close to zero in this case.
3. On the other hand, we find no conclusive evidence that gender and smoking, as well as smoking and drinking, are dependent on each other since their p-values are greater than 0.05.

Conclusion

In this blog, we have seen what is chi-square test? What is it used for? How to implement the test in python? And finally how to visualize the result? If you have any suggestions or questions feel free to comment them down. Also, connect with me on LinkedIn. Happy Learning! In future blogs I will try to cover other statistical tests like the T-test and the Anova test.

The author uses the media shown in this article at their discretion, and Analytics Vidhya does not own them.

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