When should I use Fisher's exact test instead of chi-square?

Use Fisher's exact test when any expected cell count is below 5, or when the total sample size is small (n < 20). For larger samples with adequate expected counts, chi-square gives nearly identical p-values and is computationally simpler.

What does the two-tailed p-value mean?

The two-tailed p-value is the probability of observing an association as strong as or stronger than the one in your table, in either direction, if the null hypothesis of independence is true. A p-value below 0.05 is conventionally considered statistically significant.

What is the odds ratio?

The odds ratio (OR) is (a×d)/(b×c). An OR of 1 means no association. OR > 1 means the outcome is more likely in group 1; OR < 1 means it is less likely. The 95% confidence interval tells you the range of plausible OR values.

What if a cell count is zero?

A zero count is valid — the test still works. However, if an entire row or column is zero, the odds ratio is undefined (0 or infinity) and the confidence interval cannot be computed. The p-value is still reported.

How is the exact p-value computed?

The tool enumerates all possible 2x2 tables with the same marginal totals using the hypergeometric distribution, sums the probabilities of tables whose probability is ≤ the observed table probability. This is the standard two-tailed Fisher approach.

Is my data kept private?

Yes. All computation runs entirely in your browser. No data is sent to any server.

Fisher Exact Test

Enter four cell counts in a 2x2 table and get the exact two-tailed p-value, odds ratio, and confidence interval.

2×2 Contingency Table

Row variable

Column variable

			Total
			15
			15
Total	13	17	30

Significance level (α)

Fill in the table and click Run Test to see results.

Summary

Fisher's exact test computes the precise probability of observing a contingency table as extreme as, or more extreme than, the one you entered, assuming the row and column totals are fixed and the two variables are independent. Unlike the chi-square test, it works reliably with small sample sizes and expected cell counts below 5. Enter the four observed cell counts (a, b, c, d) and the tool returns the two-tailed p-value, the odds ratio, and its 95% confidence interval.

How it works

Enter the four cell counts (a, b, c, d) for your 2x2 table.
Row and column marginal totals are computed automatically.
The exact p-value is computed by summing the hypergeometric probabilities of all 2x2 tables with the same marginals that are as extreme as or more extreme than the observed table.
Two-tailed p-value combines both tails: all tables with probability ≤ P(observed).
The odds ratio (a×d)/(b×c) measures the strength of association.
A 95% confidence interval for the odds ratio is estimated using the Woolf log-odds method.

Use cases

Determine if a new drug reduces adverse events compared to a placebo in a small clinical trial.
Test whether disease presence is associated with a binary risk factor when sample sizes are small.
Analyze a 2x2 contingency table when any expected cell count falls below 5.
Compare pass/fail rates between two groups in quality control.
Assess whether two categorical survey responses are independent.
Validate genetic association studies with rare allele frequencies.
Replace the chi-square test when the approximation assumption is violated.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu