Chi-Square Test (categorical association)

When to use

Use the chi-square test of independence when you have:

Two categorical variables
Counts in a contingency table

Example questions:

Is purchase (yes/no) associated with plan type (basic/pro)?
Is churn associated with region?

Example

Chi-square test

import pandas as pd
from scipy.stats import chi2_contingency
 
# Example contingency table
# rows: plan, columns: churn
ct = pd.DataFrame(
    {
        "churn_no": [80, 120],
        "churn_yes": [20, 60],
    },
    index=["basic", "pro"],
)
 
chi2, p, dof, expected = chi2_contingency(ct)
print("chi2:", chi2)
print("p:", p)
print("dof:", dof)
print("expected:\n", expected)

Chi-square test

import pandas as pd
from scipy.stats import chi2_contingency
 
# Example contingency table
# rows: plan, columns: churn
ct = pd.DataFrame(
    {
        "churn_no": [80, 120],
        "churn_yes": [20, 60],
    },
    index=["basic", "pro"],
)
 
chi2, p, dof, expected = chi2_contingency(ct)
print("chi2:", chi2)
print("p:", p)
print("dof:", dof)
print("expected:\n", expected)

Interpreting results

Small p-value → evidence of association
Expected counts should not be too small (rule of thumb: mostly >= 5)

Effect size (optional)

After significance, consider effect size like Cramér’s V.

How the test works

diagram Chi-square test of independence mermaid

  flowchart LR
  A["Contingency table
(observed counts)"] --> B["Expected counts
if variables were independent"]
  B --> C["Chi-square statistic
sum of (obs - exp)^2 / exp"]
  C --> D["p-value"]
  D --> E["Small p -> variables
are associated"]

Observed counts are compared against the counts you'd expect if the two variables were unrelated.

🧪 Try It Yourself

Exercise 1 – Build a contingency table

Exercise 2 – Run the chi-square test

Exercise 3 – Checking expected counts

Continue to Correlation vs Causation to measure how two numeric variables relate.

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