TimelyScholarFree Tools › Chi-Square Calculator
Run a chi-square test of independence on tables up to 5×5. You get the chi-square statistic, degrees of freedom, p-value, Cramér's V and expected counts, with a warning when counts are too small.
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| Column 1 | Column 2 | |
|---|---|---|
| Row 1 | ||
| Row 2 |
| Chi-square (χ²) | 3.922 |
|---|---|
| Degrees of freedom | 1 |
| p-value | 0.048 |
| Cramér's V (effect size) | 0.140 |
| Total N | 200 |
| 15.00 | 85.00 |
| 15.00 | 85.00 |
Choose the number of rows and columns.
Observed frequencies in each cell.
χ², df, p-value and Cramér's V in APA style.
The chi-square test of independence checks whether two categorical variables are associated, by comparing the observed counts with the counts expected if there were no association.
The test relies on reasonably large expected counts. A common rule of thumb is that no expected count should be below 1 and no more than 20% below 5; otherwise use Fisher's exact test.
Chi-square uses an approximation that needs adequate expected counts; Fisher's exact test calculates the exact probability and suits small samples.
It makes the 2×2 test more conservative. Many statisticians report the uncorrected test for moderate or large samples; follow your field's convention.