Fisher's Exact Test Calculator for a 2 by 2 Table: p-Value and Odds Ratio

An exact test for small 2 by 2 tables.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the four counts of the table.

Enter the significance level.

The calculator gives the exact p-values, the odds ratio and its interval, and a statement of the conclusion.

Formulas used

  • P = \frac{\binom{r_1}{a}\binom{r_2}{c}}{\binom{N}{c_1}}
  • OR = \frac{ad}{bc}

Worked example

With the default numbers in the calculator above:

  1. Probability of exactly this table, with the row and column totals fixed (hypergeometric): 0.023601
  2. Two-sided p-value: the total probability of all tables as unlikely or less than this one: 0.034965
  3. One-sided p-value for more in the first cell (the upper tail): 0.024476
  4. One-sided p-value for fewer in the first cell (the lower tail): 0.99913
  5. Sample odds ratio: 20
  6. 95 percent confidence interval for the odds ratio (Woolf's method): 1.416 to 282.5

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

When do I use Fisher's exact test?

For a 2 by 2 table with small counts, when any expected count is below 5 and the chi-square test is not reliable.

What is the odds ratio?

The odds of the outcome in one group divided by the odds in the other. A value of 1 means no association.

What is the difference between one-sided and two-sided?

One-sided tests for an association in one direction only. Two-sided tests for any association.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any statistics text (exact tests for contingency tables).

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