Chi-Square Test vs ANOVA: When to Use Each

Quick answer: Learn the Chi-Square test for categorical data, how it differs from ANOVA, and when to use each statistical test, with Python examples.

Chi-Square and ANOVA Solve Different Problems

Both are hypothesis tests, but they apply to fundamentally different types of data. Chi-Square tests relationships between categorical variables. ANOVA compares the means of a continuous variable across three or more groups.

What is the Chi-Square Test?

The Chi-Square test checks whether there is a statistically significant association between two categorical variables, by comparing observed frequencies in a contingency table against the frequencies you would expect if the variables were genuinely independent.

import pandas as pd
from scipy.stats import chi2_contingency

data = pd.DataFrame({
    'Program':  ['PGP', 'PGP', 'FullStack', 'FullStack'],
    'Placed':   ['Yes', 'No', 'Yes', 'No'],
    'Count':    [45, 5, 38, 12]
})

contingency_table = data.pivot_table(index='Program', columns='Placed', values='Count')
chi2, p_value, dof, expected = chi2_contingency(contingency_table)

print(f"Chi-square: {chi2:.2f}, p-value: {p_value:.4f}")

A low p-value here would suggest program choice and placement outcome are genuinely associated, rather than independent of each other.

A Quick Reminder: What ANOVA Tests

from scipy import stats

pgp_scores = [78, 82, 85, 90, 76]
fullstack_scores = [65, 70, 72, 68, 74]
analytics_scores = [88, 91, 85, 93, 89]

f_stat, p_value = stats.f_oneway(pgp_scores, fullstack_scores, analytics_scores)

Key Differences

Choosing the Right Test: A Simple Rule

Ask what type your outcome variable is. If it is categorical, such as pass or fail, use Chi-Square. If it is continuous, such as an exam score, and you are comparing across three or more groups, use ANOVA. If comparing exactly two groups on a continuous outcome, use a t-test instead.

A Second Use of Chi-Square: Goodness of Fit

Beyond testing association between two categorical variables, Chi-Square can also test whether a single categorical variable's observed distribution matches an expected distribution, such as checking whether website traffic is evenly split across four regions as expected.

Common Interview Questions

How do you decide between Chi-Square and ANOVA for a given problem?

Look at the outcome variable's type. Chi-Square applies when both variables of interest are categorical. ANOVA applies when the outcome is continuous and you are comparing means across three or more groups.

What does a significant Chi-Square result actually mean?

It means the two categorical variables are unlikely to be independent, suggesting a genuine association exists between them, though it does not by itself indicate the strength or direction of that association.