Fisher Exact Test Calculator
Fisher Exact Test is a statistical significance test used to analyze contingency tables when sample sizes are small. It calculates the exact probability of observing a particular distribution of frequencies in a 2x2 table, assuming the null hypothesis of independence. Unlike chi-square tests, it's particularly useful for small datasets (typically when any cell count is less than 5) as it doesn't rely on approximations. Researchers commonly use it in biology, medicine, and social sciences to assess associations between categorical variables.
Formula
The probability (p-value) for Fisher's Exact Test is calculated using the hypergeometric distribution:
p = ( (a+b)! (c+d)! (a+c)! (b+d)! ) / ( a! b! c! d! n! )
Where n = a + b + c + d (total observations)
Advantages and Disadvantages
Advantages:
1. Provides exact p-values without relying on approximations, making it ideal for small sample sizes
2. No minimum sample size requirement
3. Particularly effective when dealing with rare events or unbalanced designs
4. Appropriate for all 2x2 contingency tables regardless of marginal frequencies
5. Exact nature makes it universally acceptable for publication
Disadvantages:
1. Computationally intensive for large sample sizes
2. Limited to 2x2 tables in most implementations
3. Can be conservative in practice
4. Requires fixed marginal totals which may not reflect real experimental designs
5. Interpretation challenges with mid-p values
While Fisher's Exact Test is valuable for small samples, its requirement for fixed margins can lead to misinterpretation. The assumption that marginal totals are fixed experimental parameters often doesn't hold in observational studies. For large datasets, the computational complexity increases exponentially, making chi-square tests more practical. Additionally, the test's exact nature can sometimes be too conservative, potentially missing true effects. Despite these limitations, it remains the gold standard for analyzing small 2x2 contingency tables where approximation methods fail.