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What is Fisher's Exact Test?

Fisher's exact test is a statistical significance test used to determine whether there is a non-random association between two categorical variables in a 2×2 contingency table. Unlike the chi-square test, which relies on a large-sample approximation, Fisher's exact test computes the exact probability of observing the data (or more extreme data) under the null hypothesis of independence. This makes it especially appropriate when sample sizes are small or when expected cell frequencies fall below 5.

When to Use Fisher's Exact Test

Use Fisher's exact test instead of the chi-square test when one or more of the following conditions apply: your total sample size is small (typically N < 20-30), any expected cell frequency is below 5, or you have a 2×2 table with highly unbalanced marginals. It is the gold standard for small-sample categorical analysis and is commonly used in clinical trials, epidemiology, and biomedical research where sample sizes may be limited.

Fisher's Exact Test vs. Chi-Square Test

Assumptions of Fisher's Exact Test

Fisher's exact test has fewer assumptions than the chi-square test, but the following must still be met:

Understanding the Odds Ratio

The odds ratio (OR) quantifies the strength and direction of the association in a 2×2 table. It compares the odds of the outcome in one group to the odds in the other group:

How to Report Fisher's Exact Test in APA Format

When reporting Fisher's exact test results in APA format, include the test name, p-value, odds ratio, and 95% confidence interval:

Note: Report p-values to three decimal places, using p < .001 when below that threshold. Always include the odds ratio and its 95% confidence interval. If any cell contains zero, note that the odds ratio may be undefined or infinite.

Common Mistakes to Avoid

• Using chi-square with small samples: When expected frequencies are below 5, the chi-square approximation is unreliable. Fisher's exact test should be used instead for 2×2 tables with small samples.
• Ignoring the confidence interval: A significant p-value alone does not tell you the magnitude of the effect. Always report the odds ratio with its 95% confidence interval to convey both the direction and uncertainty of the association.
• Confusing odds ratio with relative risk: The odds ratio and relative risk are different measures. When the outcome is common (> 10%), the odds ratio overestimates the relative risk. Report both when appropriate.
• Applying to non-binary data: Fisher's exact test is designed for 2×2 tables. For larger tables, use the chi-square test or the Freeman-Halton extension.
• Using with paired data: Fisher's exact test assumes independent observations. For paired or matched binary data, use McNemar's test.