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 contingency table. It is particularly useful when sample sizes are small, allowing researchers to evaluate the significance of the observed frequencies in relation to the expected frequencies under the null hypothesis, which states that there is no association between the variables. This test provides an exact p-value rather than an approximation, making it valuable in situations where traditional chi-square tests may not be applicable.

5 Must Know Facts For Your Next Test

1. Fisher's exact test is commonly applied in studies involving small sample sizes where expected frequencies are less than five, which can invalidate chi-square tests.
2. This test calculates the exact probabilities of obtaining the observed distribution of counts across the contingency table under the assumption of independence between the variables.
3. The p-value obtained from Fisher's exact test directly indicates whether the observed differences in proportions are statistically significant or not.
4. In a 2x2 contingency table, Fisher's exact test can be computed using combinatorial mathematics, making it computationally intensive for larger tables.
5. The test is named after Ronald A. Fisher, who introduced it in 1922 as a method to address issues related to small sample sizes in statistical analysis.

Review Questions

• How does Fisher's exact test differ from chi-square tests when analyzing data from contingency tables?
  • Fisher's exact test differs from chi-square tests primarily in its application to small sample sizes. While chi-square tests rely on large samples and approximations to determine significance, Fisher's exact test calculates exact probabilities based on the observed frequencies, making it more reliable for smaller datasets. This ensures that researchers can still evaluate associations between categorical variables without violating assumptions required by chi-square tests.
• In what scenarios would you prefer using Fisher's exact test over other statistical tests for analyzing categorical data?
  • Fisher's exact test is preferred in scenarios where sample sizes are small and when the expected frequency of one or more cells in a contingency table is less than five. It is particularly useful when dealing with rare events or when examining rare diseases in medical research. By providing an exact p-value rather than relying on asymptotic approximations, this test allows for more accurate conclusions about the association between categorical variables, especially when dealing with limited data.
• Evaluate how Fisher's exact test contributes to research involving rare events and its implications for scientific conclusions.
  • Fisher's exact test plays a crucial role in research involving rare events by enabling researchers to make valid statistical inferences even with limited sample sizes. By providing an exact calculation of p-values, it ensures that researchers can confidently assess whether observed associations are statistically significant or due to chance. This ability is essential in fields like epidemiology or clinical trials where events of interest are infrequent. Consequently, using Fisher's exact test can lead to more robust scientific conclusions and better decision-making based on evidence derived from small samples.

Related terms

Contingency Table:

A table used to display the frequency distribution of variables, helping to summarize categorical data and analyze the relationship between different categories.

P-value: A measure that helps determine the strength of evidence against the null hypothesis in a statistical test, indicating the probability of observing the data if the null hypothesis is true.

Null Hypothesis: A statement in statistical testing that assumes no effect or no association between variables, serving as a baseline for comparison with observed data.