Fisher's Exact Test Calculator

What Is Fisher's Exact Test?

Fisher's exact test checks independence between two categorical variables in a 2×2 contingency table. It is preferred over the chi-square test when sample sizes are small or expected cell counts fall below five. Try the Chi-Square Test Calculator for larger tables.

Hypergeometric Probability Formula

Under the null hypothesis of independence, the probability of observing cell counts $a$, $b$, $c$, $d$ is:

$$P = \frac{(a+b)!\,(c+d)!\,(a+c)!\,(b+d)!}{a!\,b!\,c!\,d!\,n!}$$

where $n = a + b + c + d$. The p-value sums probabilities of tables as extreme as (or more extreme than) the observed table.

When to Use Fisher's Exact Test

Use Fisher's exact test for 2×2 tables with small totals, uneven marginals, or any cell count below five. For larger balanced tables, the chi-square approximation is usually sufficient and faster to compute.