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Local calculation
Free browser-based statistical calculator
Chi Square Test Calculator 3x2
Enter a 3×2 contingency table to calculate the chi-square statistic, p-value, expected counts, Cramér’s V, standardized residuals, and Fisher–Freeman–Halton exact test.
Six-count input
Exact test when needed
Copy-ready report
Runs in your browser
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Ready
Results
Chi-square (χ²)—
Degrees of freedom—
P-value—
Sample size (N)—
Cramér’s V—
Conclusion
Enter your six counts and select Calculate chi-square.
Your detailed results will include expected counts, assumption checks, an exact test when needed, and a copy-ready interpretation.
Assumption check
- Minimum expected count
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- Cells below 5
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Fisher–Freeman–Halton exact test
The exact test result will appear here when the expected-count check recommends it.
- Exact p-value
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- Tables evaluated
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Cell-level analysis
Observed and expected counts
Large standardized residuals identify cells contributing most strongly to the association.
| Cell | Observed | Expected | Residual | χ² contribution |
|---|
Ready for your paper or report
Copy-ready result
Pearson chi-square
Instant statistic, degrees of freedom, and p-value.
Assumption check
Expected-count rules are checked automatically.
Exact test
Fisher–Freeman–Halton is calculated for sparse tables.
Effect size
Cramér’s V shows the strength of association.
How it works
Calculate a 3×2 chi-square test in four steps
- 1Enter six observed counts
Add three groups in rows and two outcome categories in columns.
- 2Calculate the test
The calculator derives expected counts, χ², df = 2, and the right-tail p-value.
- 3Review assumptions and effect size
See minimum expected counts, Cramér’s V, and standardized residuals.
- 4Copy the interpretation
Use the generated sentence in a report, paper, or analysis note.
Frequently asked questions
3×2 chi-square test questions
What is a 3×2 chi-square test?
It tests whether a three-category group variable is associated with a two-category outcome variable. Common examples include three treatments by improved/not improved and three age groups by yes/no.
Is a 3×2 table the same as a 2×3 table?
Yes. Transposing the rows and columns preserves the chi-square statistic, degrees of freedom, p-value, and Cramér’s V.
What are the degrees of freedom?
A 3×2 table has 2 degrees of freedom because (rows − 1) × (columns − 1) = (3 − 1) × (2 − 1).
Should I enter counts or percentages?
Enter the six observed whole-number counts. The calculator uses these values to derive row totals, column totals, expected counts, and effect size.
When is the exact test calculated?
The calculator checks every expected count. When the table is sparse, it calculates the Fisher–Freeman–Halton exact p-value using the same fixed row and column totals.