2×3 Fisher Exact Test Calculator (Fisher–Freeman–Halton)
Enter your observed counts for a 2×3 contingency table. This tool computes the exact two-sided p-value by conditioning on fixed row and column totals.
Use whole numbers only (0, 1, 2, ...). Best for small sample sizes where chi-square assumptions may be weak.
| Category 1 | Category 2 | Category 3 | |
|---|---|---|---|
| Group A | |||
| Group B |
What is a 2×3 Fisher exact test?
A 2×3 Fisher exact test is an extension of the classic Fisher exact test used for 2×2 tables. In this case, you have two groups (rows) and three outcome categories (columns). The test asks whether the outcome distribution is independent of group membership, given fixed margins.
Why use this instead of chi-square?
The chi-square test is an approximation. It usually performs well when sample sizes are large and expected counts are not too small. But with sparse data, small samples, or highly uneven counts, an exact method is safer. This calculator performs the exact conditional test, commonly called the Fisher–Freeman–Halton test for RxC tables.
Good use cases
- Clinical pilot studies with small enrollment.
- Survey data split into two groups with three response levels.
- Any 2×3 table where one or more expected counts are low.
How to interpret the p-value
The p-value is the probability, under the null hypothesis of independence, of observing a table at least as unlikely as yours (using the exact conditional reference set with the same margins). A small p-value suggests evidence against independence.
- p < 0.05: evidence of association between row group and column category.
- p ≥ 0.05: insufficient evidence to claim association.
Remember: a p-value does not measure effect size. It only measures incompatibility with the null model.
Practical tips for reporting
- Report the full 2×3 table, not just the p-value.
- State that you used an exact Fisher–Freeman–Halton test.
- Include row/column percentages so readers can see the direction of differences.
- If needed, follow up with planned pairwise comparisons and multiple-testing correction.
Assumptions and notes
- Data are counts in mutually exclusive categories.
- Observations are independent within and between groups.
- Margins are treated as fixed for the exact conditional calculation.
- This calculator returns a two-sided exact p-value based on table probabilities.
Example
Suppose Group A has counts (8, 3, 1) and Group B has counts (2, 5, 7). The calculator enumerates all 2×3 tables with the same margins and sums probabilities less than or equal to the observed table probability. That sum is your exact two-sided p-value.
FAQ
Can I use decimals?
No. This is a count-based test, so values must be non-negative integers.
Can this be used for larger tables?
This page is specifically for 2×3. Larger RxC exact tests are possible but computationally heavier.
Does a non-significant result prove no effect?
No. It means your data do not provide strong enough evidence against independence at your chosen threshold.