Chi-Square Test Calculator - Goodness of Fit & Test of Independence
Chi-Square Test Calculator
Goodness of fit and contingency-table tests with exact p-values
Two Tests
Check whether counts match an expected distribution, or whether two categorical variables in a table are related.
Paste from a Spreadsheet
Copy a block of cells and paste it straight into the table box; tabs and spaces both work.
Assumption Check
Expected counts below 5 are flagged, because the chi-square approximation becomes unreliable there.
Private
Your data stays in your browser.
How the Chi-Square Test Works
Both tests compare observed counts O with the counts E you would expect if the null hypothesis were true, adding up (O − E)2/E over every category or cell. In a goodness-of-fit test, E comes from the distribution you specify (equal by default) and there are k − 1 degrees of freedom. In a test of independence, E for each cell is (row total × column total) / grand total and the degrees of freedom are (rows − 1)(columns − 1).
Example: a die rolled 120 times gives 22, 17, 21, 12, 14 and 34. With 20 expected per face, χ2 = 15.5 with 5 degrees of freedom and p ≈ 0.0084, so the die looks unfair at the 5% level. Use raw counts, never percentages or means, in the observed boxes. Cramér's V, from 0 to 1, shows how strong an association is, which a small p-value alone does not.
Key Takeaways
- Counts only: The observed values must be frequencies, not percentages.
- Expected at least 5: Small expected counts are flagged; merge categories if needed.
- Effect size: Cramér's V shows how strong an association is.