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Fisher Exact Test Calculator

Calculate the Fisher exact test probability for a 2×2 contingency table.

About Fisher Exact Test Calculator

Fisher’s exact test computes the hypergeometric probability directly, making it valid at any sample size. Logarithms of factorials are used to avoid overflow with larger counts. Chi-square becomes unreliable when any expected count falls below five, which is exactly when Fisher’s exact test should be used instead.

Formula

Fisher Exact Test

P = (r₁! r₂! c₁! c₂!) ÷ (N! a! b! c! d!) for the hypergeometric probability of one table

exact test
Computes probability directly rather than approximating
expected count
Row total × column total ÷ grand total

Worked example

With the default values below, Fisher Exact Test Calculator returns Probability of This Exact Table of 0.03215051. Change any input above and every figure here is recalculated in your browser.

Inputs used

Cell Aaccepts 0–200
8
Cell Baccepts 0–200
2
Cell Caccepts 0–200
3
Cell Daccepts 0–200
7

Results

Probability of This Exact Table
0.03215051
Odds Ratio
9.33333
Total Observations
20
Expected Value of Cell A
5.5000
Recommendation
Chi-square would also be valid at these counts

Step by step

  1. 1Values used
  2. 2Fisher Exact Test
  3. 3Probability of This Exact Table= 0.03215051
  4. 4Odds Ratio= 9.33333
  5. 5Total Observations= 20
  6. 6Expected Value of Cell A= 5.5000
  7. 7Recommendation= Chi-square would also be valid at these counts

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Fisher Exact Test calculated?

P = (r₁! r₂! c₁! c₂!) ÷ (N! a! b! c! d!) for the hypergeometric probability of one table Fisher’s exact test computes the hypergeometric probability directly, making it valid at any sample size. Logarithms of factorials are used to avoid overflow with larger counts.

Why does Fisher Exact Test matter?

Chi-square becomes unreliable when any expected count falls below five, which is exactly when Fisher’s exact test should be used instead.

What values do I need to enter?

This calculator takes 4 inputs: Cell A, Cell B, Cell C, Cell D. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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