What is the null hypothesis of this test?

The null hypothesis is that the two categorical variables are independent — knowing the value of one tells you nothing about the other. A small p-value gives evidence to reject this hypothesis.

What p-value threshold should I use?

The conventional threshold is 0.05 (5%). If p < 0.05 the result is considered statistically significant and you reject the null hypothesis of independence. Some fields use 0.01 or 0.10.

When is the chi-square test not valid?

The test assumes all expected cell counts are at least 5. If any expected count falls below 5, use Fisher's exact test instead. The tool warns you when this condition is violated.

What are degrees of freedom?

Degrees of freedom (df) = (number of rows - 1) × (number of columns - 1). For a 2x2 table, df = 1. Degrees of freedom determine which chi-square distribution is used to find the p-value.

Can I use more than 2 rows or columns?

Yes. Use the "Rows" and "Columns" controls to expand the table up to 6x6. The test works for any r×c contingency table as long as expected counts are adequate.

Does the tool apply Yates' correction?

Yates' continuity correction is optionally applied for 2x2 tables, which slightly reduces the chi-square statistic. Toggle it with the checkbox that appears for 2x2 tables.

Chi-Square Independence Test

Name: Chi-Square Independence Test
Availability: InStock
Author: Nham Vu

Enter observed counts in a contingency table to compute the chi-square statistic, degrees of freedom, and p-value for testing independence.

Contingency Table

Rows

Columns

Row variable label

Column variable label

Apply Yates’ continuity correction (2x2 only)

Significance level (α)

Fill in the table and click Run Test to see results.

Summary

Enter observed counts in a contingency table to compute the chi-square statistic, degrees of freedom, and p-value for testing independence.

How it works

Choose the number of rows and columns for your contingency table (default 2x2).
Enter the observed frequency counts in each cell.
Click "Run Test" to compute row and column totals.
The tool calculates expected counts using the formula: (row total × column total) / grand total.
The chi-square statistic is the sum of (observed - expected)^2 / expected across all cells.
Degrees of freedom = (rows - 1) × (columns - 1). The p-value is derived from the chi-square distribution.

Use cases

Test whether a marketing campaign response rate differs across age groups.
Determine if product preference is independent of gender.
Analyze whether disease occurrence is associated with a risk factor.
Evaluate whether survey responses differ between regions.
Check independence of two classification variables in a research dataset.
Validate assumptions before applying further statistical models.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu