Statistical test · BEGINNER LESSON
Fisher's exact test
Fisher's exact test is an exact statistical test for a 2×2 table of binary outcomes. It tests whether the two variables are independent, using the observed table margins and the hypergeometric distribution.
What it is and what it measures
Fisher's exact test is used for a two-way contingency table with two binary variables, such as presence or absence of two events. It measures whether the pattern in the 2×2 table is more extreme than expected if the variables were independent. The test gives an exact p-value for the null hypothesis of no association, and it is often used when sample size is limited.
[1] Interpreting Mutation Co-Occurrence in Cancer Genomics Under ... [2] Bias of Odds Ratio Estimate in Fisher's Exact Test - PMC
How it works
The method conditions on the observed row and column totals, then uses the hypergeometric distribution to compute the probability of the observed table and equally or more extreme tables. This makes the p-value exact under the null model. The test is often described as testing whether the odds ratio equals 1 under the null hypothesis. In practice, the odds ratio can be reported with an exact confidence interval.
[2] Bias of Odds Ratio Estimate in Fisher's Exact Test - PMC
What the result means in biology studies
In cohort-level mutation studies, Fisher's exact test can ask whether two binary alterations are associated across samples. A significant result suggests the table is unlikely under independence, but it does not show physical localization within the same cell. In bulk sequencing, seeing both alterations only shows they are present in the analyzed material, not that they occur in the same cell.
[1] Interpreting Mutation Co-Occurrence in Cancer Genomics Under ...
Limitations
Fisher's exact test does not account for factors such as sample-specific mutation burden, gene-specific alteration probability, tumor subtype, or cohort composition. So heterogeneous data can create misleading association or exclusivity signals. The odds ratio estimate from the test can be biased and may even become undefined or infinite when some cells are zero. The test is also different from methods for paired data, such as the McNemar test, which are designed for matched observations rather than independent groups.
[1] Interpreting Mutation Co-Occurrence in Cancer Genomics Under ... [2] Bias of Odds Ratio Estimate in Fisher's Exact Test - PMC [3] Clinical Significance
SEE THE IDEA
How Fisher's exact test analyzes a 2×2 table
Counts two yes/no variables in four cells.
Row and column totals are treated as given.
Calculates the exact probability of the observed table under independence.
Summarizes how unusual the table is under the null hypothesis.
The table margins feed the exact probability model, which produces the p-value.
Fisher's exact test turns a 2×2 count table into an exact probability statement about independence.
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.