Fisher's Exact Test Calculator
Calculate exact p-values for 2×2 contingency tables and test independence of categorical variables
2×2 Contingency Table
Enter the observed frequencies for each cell in your 2×2 contingency table:
Two-tailed tests for any association; one-tailed tests for directional association
Example: Gender vs Sport Preference
Study Data
A study of 11 people examined whether sport preference (cycling vs swimming) is associated with gender.
Sample: 5 men and 6 women
Results: 1 man chose swimming, 4 men chose cycling, 4 women chose swimming, 2 women chose cycling
Contingency Table
Results
One-tailed p-value: 0.175324
Two-tailed p-value: 0.242424
Interpretation: No significant association between gender and sport preference (p > 0.05)
When to Use Fisher's Exact Test
Small Sample Size
When any expected frequency < 5
2×2 Contingency Table
Two categorical variables with two levels each
Exact Results
When you need exact p-values, not approximations
Unbalanced Data
When marginal totals are very uneven
P-value Interpretation
Understanding Fisher's Exact Test
What is Fisher's Exact Test?
Fisher's exact test is a statistical test for independence between two categorical variables in a 2×2 contingency table. Unlike the chi-squared test, it provides exact p-values rather than approximations, making it ideal for small samples.
Key Features
- •Provides exact p-values based on hypergeometric distribution
- •Does not rely on normal approximations
- •Suitable for any sample size, especially small samples
- •Tests the null hypothesis of independence between variables
Formula and Calculation
P = (a+b)!(c+d)!(a+c)!(b+d)! / (a!b!c!d!n!)
Where a, b, c, d are the cell frequencies and n is the total sample size.
One-tailed vs Two-tailed
- Two-tailed: Tests for any association (positive or negative)
- One-tailed: Tests for association in a specific direction
- Recommendation: Use two-tailed unless you have a strong theoretical reason for one-tailed
Fisher's Exact Test vs Chi-squared Test
Use Fisher's Exact Test when:
- • Any expected frequency < 5
- • Small sample sizes (n < 20-30)
- • Very unbalanced margins
- • Need exact p-values
Use Chi-squared Test when:
- • All expected frequencies ≥ 5
- • Large sample sizes
- • Computational efficiency needed
- • Tables larger than 2×2