Fisher's exact (2×2)
§2.2
Rev 4.6 · reviewed Feb 2026Fisher's exact test (2×2)
The exact alternative to chi-square when any expected cell count is small (< 5). No large-sample approximation — it enumerates every table with your margins.
Source formula: Fisher RA. Statistical Methods for Research Workers. 1925.
Table. Outcome by group
| Outcome + | Outcome − | Total | |
|---|---|---|---|
| Group 1 | 20 | ||
| Group 2 | 20 | ||
| Total | 10 | 30 | 40 |
* Two-sided exact p by the sum of tables no more probable than observed. Fisher RA. Statistical Methods for Research Workers. 1925.
† Proportion CIs are Wilson intervals. Wilson EB. J Am Stat Assoc 1927;22:209–12.
Group 1 proportion (95% CI)†
10.0% (2.8%–30.1%)
copyGroup 2 proportion (95% CI)†
40.0% (21.9%–61.3%)
copyOdds ratio
0.17
copyTwo-sided exact p
0.065
copyWith exact p = 0.065, this sample doesn't show a significant difference. With small counts, absence of significance is especially weak evidence of no effect — a wider study may be needed.
Understand what this is measuring