Chi-Square Test of Independence Calculator
Tests whether two categories are related, from a table of counts.
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
The formula
χ² = Σ (observed − expected)² ÷ expected expected = row total × column total ÷ grand total df = (rows − 1)(columns − 1)
Cramér’s V scales the result from 0 to 1, as a rough measure of the strength of association.
What to watch out for
Use raw counts, not percentages, and count each item once. Statistical software may apply Yates’ continuity correction to a 2×2 table by default, which makes its result slightly different from this one.
Frequently Asked Questions
How do I enter the table?
Row by row, with semicolons between rows. A table with rows of 10, 10, 20 and 20, 20, 20 is typed as: 10 10 20; 20 20 20.
What is a worked example?
That table gives χ² = 2.778 with 2 degrees of freedom, and p = 0.24935.
What is the critical value for 1 degree of freedom at 5%?
3.841.