What is Fisher's Exact Test?
Fisher's Exact Test is a statistical test used to determine if there are nonrandom associations between two categorical variables. It is particularly useful in the field of
epidemiology for analyzing contingency tables, especially when sample sizes are small. Unlike the
Chi-square test, Fisher's Exact Test does not rely on large sample approximations, making it ideal for small datasets.
When is Fisher's Exact Test Applied in Epidemiology?
In epidemiology, Fisher's Exact Test is often applied when researchers are dealing with small sample sizes. This could include studies with limited numbers of cases and controls, or rare
disease occurrences. For example, if researchers are studying the association between a rare genetic mutation and the occurrence of a specific disease, the sample size might be too small for a Chi-square test to be valid.
How Does Fisher's Exact Test Work?
The test works by calculating the exact probability of obtaining the observed data (and any more extreme) under the null hypothesis that the row and column variables are independent. It uses a hypergeometric distribution to derive this probability. The calculations, while straightforward, can be computationally intensive, which is why software tools are often employed for this purpose.
Advantages of Fisher's Exact Test
1. Accuracy: Fisher's Exact Test provides exact p-values, making it more reliable than other tests that rely on approximations, such as the Chi-square test.
2. Small Sample Sizes: It is particularly advantageous in situations with small sample sizes where other tests may not be appropriate.
3. No Assumptions About Distribution: The test does not assume a normal distribution of the data, making it more versatile.Limitations of Fisher's Exact Test
1. Computational Intensity: The test can be computationally demanding, especially with larger datasets.
2. Interpretation: The exact p-values can sometimes be difficult to interpret in the context of broader epidemiological studies.
3. Not Suitable for All Data: While ideal for small samples, the test may not be the best choice for very large datasets where other methods might be more efficient.Practical Applications in Epidemiology
One practical application of Fisher's Exact Test in epidemiology is in case-control studies. For instance, researchers might use the test to examine the relationship between a specific
risk factor and a health outcome. Another application is in outbreak investigations, where the test can be used to identify statistically significant associations between exposure and illness.
Example Case Study
Imagine a study investigating the association between exposure to a particular chemical and the development of a rare disease. Suppose the sample size is small: 10 exposed individuals and 10 unexposed. Fisher's Exact Test can be used to determine whether the observed distribution of disease cases between the exposed and unexposed groups is statistically significant.Steps for Conducting Fisher's Exact Test
1. Data Collection: Gather data and organize it into a 2x2 contingency table.
2. Hypothesis Setting: Formulate the null hypothesis (no association between variables) and the alternative hypothesis (association exists).
3. Calculate Test Statistic: Use statistical software or manual calculations to determine the p-value.
4. Interpret Results: Compare the p-value to the significance level (e.g., 0.05) to accept or reject the null hypothesis.Conclusion
Fisher's Exact Test is a powerful tool in the epidemiologist's toolkit, especially for analyzing small datasets and rare events. Its ability to provide exact p-values without relying on large sample approximations makes it invaluable in specific contexts. However, researchers must also be aware of its computational demands and limitations to apply it appropriately.
