Fisher Exact Test

Summary

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

How it works

1. Enter the four cell counts (a, b, c, d) for your 2x2 table.
2. Row and column marginal totals are computed automatically.
3. 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.
4. Two-tailed p-value combines both tails: all tables with probability ≤ P(observed).
5. The odds ratio (a×d)/(b×c) measures the strength of association.
6. A 95% confidence interval for the odds ratio is estimated using Cornfield's 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