Fisher’s Exact Test Calculator
Enter the 2 × 2 contingency table
Use non-negative whole-number counts. Rows represent groups; columns represent the two outcomes.
Group
Outcome +
Outcome −
Row total
Group 1
8
Group 2
5
Column total
7
6
13
0.050
H₀: odds ratio = 1. H₁: odds ratio ≠ 1.
Exact p-value
0.102564
Not significant at α = 0.050
The exact evidence is not sufficient to reject the null hypothesis at the selected significance level.
Sample odds ratio
12.000
Cross-product estimate: ad / bc
Conditional MLE odds ratio
9.469
Conditional on fixed margins
Exact conditional 95% CI
0.536 – 686.484
Central interval for the odds ratio
Observed-table probability
0.0815851
Hypergeometric probability of this table
Risk ratio
3.750
Descriptive: P(+|Group 1) / P(+|Group 2)
Phi coefficient (φ)
0.5367
Signed association for a 2 × 2 table
Expected counts and diagnostics
Expected counts are shown for context. Fisher’s exact test does not rely on the large-sample expected-count approximation.
Group 1, Outcome +
4.308
Group 1, Outcome −
3.692
Group 2, Outcome +
2.692
Group 2, Outcome −
2.308
Minimum expected count = 2.308. Exact inference is useful when samples or expected counts are small.
Exact null distribution
Each bar is the probability of a possible upper-left cell count while keeping the observed margins fixed.
Possible tables
Included in selected p-value
Observed table
