Fisher's exact test checks association in a 2×2 table without relying on the chi-square approximation.
Why it matters
When counts are small, chi-square can be wrong. Fisher's test is exact.
Key ideas
- For 2×2 tables with small expected counts
- Uses exact probabilities of the table
- Gives the odds ratio and its CI
- Works for any sample size, but is mostly needed for small ones
- p is usually two-sided
- Larger r×c tables need an extension
Real-life research example
In a pilot of 14 patients, 6 of 7 on a new drug improved vs 2 of 7 on standard care.
When to use
- 2×2 table where some expected counts are below 5
When NOT to use
- Don't use chi-square when expected counts are tiny
- Don't use for paired yes/no (use McNemar)
Mini example
Drug: 6 improved, 1 not; Standard: 2 improved, 5 not
Quick takeaway
Small counts → Fisher, not chi-square.
Try it yourself
Enter the counts above. Compare Fisher's p with the chi-square p. Which one would you report?
Model answer
Several expected counts are below 5, so report Fisher's exact p. Chi-square would be unreliable here.