Fisher's Exact Test calculator

Calculate exact p-values for a 2x2 contingency table. Ideal for small sample sizes where Chi-square fails.

What it does

Tests association in a 2×2 table by enumerating every arrangement of the data with the same margins, giving an exact p-value with no large-sample approximation.

When to use it

Small samples or sparse tables, particularly when any expected cell count falls below about 5 and chi-square becomes unreliable.

Cautions

• It conditions on the observed margins, which makes it noticeably conservative — real effects can go undetected in small samples.
• Exact does not mean assumption-free: observations must still be independent.
• Report the odds ratio with its interval; the p-value alone does not convey how large the association is.

Alternatives

• Chi-square test of independence — the table is large and expected counts are comfortable
• McNemar's test — the two columns are paired measurements on the same subjects

How to read the output

When it is used here

The chi-square module computes it automatically for a 2×2 table whenever an expected count falls below 5, and flags that it did. It is exact in the sense of not relying on a large-sample approximation — not in the sense of being more correct. It is conservative: its p-value tends to be larger than the true error rate, so it can miss real associations that chi-square would find.

It gives a p-value, not an effect size

The size of the association comes from the odds ratio or risk ratio, which the chi-square module reports beside it for a 2×2. With counts small enough to need an exact test, those measures have very wide intervals. Report the interval rather than the p-value — "no significant difference" from a handful of events almost always means the study could not have detected one.

Larger tables

It is offered for 2×2 tables only. Collapsing a larger table down to 2×2 to force an exact test costs you the distinction you collapsed. That is a decision about the subject matter, and it has to be made before seeing the p-value rather than after.

How this calculator is validated · Which statistical test should I use?