A Chi-Square Test of Independence is used to determine whether or not there is a significant association between two categorical variables.
This tutorial explains how to perform a Chi-Square Test of Independence in Python.
Example: Chi-Square Test of Independence in Python
Suppose we want to know whether or not gender is associated with political party preference. We take a simple random sample of 500 voters and survey them on their political party preference. The following table shows the results of the survey:
Republican | Democrat | Independent | Total | |
Male | 120 | 90 | 40 | 250 |
Female | 110 | 95 | 45 | 250 |
Total | 230 | 185 | 85 | 500 |
Use the following steps to perform a Chi-Square Test of Independence in Python to determine if gender is associated with political party preference.
Step 1: Create the data.
First, we will create a table to hold our data:
data = [[120, 90, 40], [110, 95, 45]]
Step 2: Perform the Chi-Square Test of Independence.
Next, we can perform the Chi-Square Test of Independence using the chi2_contingency function from the SciPy library, which uses the following syntax:
chi2_contingency(observed)
where:
- observed: A contingency table of observed values.
The following code shows how to use this function in our specific example:
import scipy.stats as stats #perform the Chi-Square Test of Independence stats.chi2_contingency(data) (0.864, 0.649, 2, array([[115. , 92.5, 42.5], [115. , 92.5, 42.5]]))
The way to interpret the output is as follows:
- Chi-Square Test Statistic: 0.864
- p-value: 0.649
- Degrees of freedom: 2 (calculated as #rows-1 * #columns-1)
- Array: The last array displays the expected values for each cell in the contingency table.
Recall that the Chi-Square Test of Independence uses the following null and alternative hypotheses:
- H_{0}: (null hypothesis) The two variables are independent.
- H_{1}: (alternative hypothesis) The two variables are not independent.
Since the p-value (.649) of the test is not less than 0.05, we fail to reject the null hypothesis. This means we do not have sufficient evidence to say that there is an association between gender and political party preference.
In other words, gender and political party preference are independent.