Fisher's Exact Test

Definition

Fisher's Exact Test is a statistical significance test used to determine if there are nonrandom associations between two categorical variables in a 2x2 contingency table. This test is particularly useful when sample sizes are small, as it calculates the exact probability of observing the data, given the null hypothesis of no association. It's a powerful tool in inferential statistics and hypothesis testing for analyzing data where traditional tests may not be valid due to small sample sizes or low frequencies.

5 Must Know Facts For Your Next Test

1. Fisher's Exact Test is applicable when the expected frequency in any of the cells of a contingency table is less than 5, making it a go-to method for small sample sizes.
2. The test operates under the hypergeometric distribution, providing an exact p-value rather than an approximation, which is essential for accurate inference.
3. It can be extended to larger contingency tables (not just 2x2), but its application is most straightforward and common in the 2x2 case.
4. Fisher's Exact Test does not rely on large-sample approximations, making it robust against violations of assumptions found in tests like Chi-square.
5. Interpreting the results involves comparing the p-value obtained from Fisher's Exact Test against a significance level (commonly set at 0.05) to make decisions regarding the null hypothesis.

Review Questions

• How does Fisher's Exact Test differ from other statistical tests used for categorical data analysis?
  • Fisher's Exact Test differs from other tests, like the Chi-square test, primarily in its applicability to small sample sizes and its use of exact probabilities. While Chi-square relies on large-sample approximations and may yield inaccurate results when expected frequencies are low, Fisher's Exact Test computes precise p-values based on the hypergeometric distribution, ensuring validity regardless of sample size. This makes Fisher's method particularly valuable when analyzing data with limited observations.
• What assumptions must be met for Fisher's Exact Test to be appropriately applied in research studies?
  • Fisher's Exact Test requires that the data being analyzed is categorical and organized into a 2x2 contingency table. Unlike other tests, it does not assume that sample sizes must be large or that expected cell frequencies are above certain thresholds. Additionally, independence among observations is crucial; each observation must belong to only one category without influencing others. These assumptions ensure that the test results are reliable and interpretable.
• Evaluate the practical implications of using Fisher's Exact Test in public health research, especially when dealing with rare diseases or outcomes.
  • Using Fisher's Exact Test in public health research has significant practical implications, especially for studies involving rare diseases or outcomes where sample sizes tend to be small. This test allows researchers to accurately assess associations between exposure and outcome without being constrained by large-sample requirements. As public health often involves understanding relationships within limited datasets—like those found in case-control studies—Fisher's Exact Test offers a precise statistical method to draw meaningful conclusions that can inform policy and intervention strategies. Its robustness in these situations ensures that even small-scale studies contribute valuable insights into public health challenges.

Related terms

Contingency Table: A table used to display the frequency distribution of variables, allowing for the examination of relationships between categorical variables.

Null Hypothesis: A statement that there is no effect or no difference, often represented as a starting point for statistical testing.

P-Value: A measure that helps determine the significance of results in hypothesis testing, indicating the probability of observing the data if the null hypothesis is true.