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's especially useful when sample sizes are small, providing a way to evaluate the independence of variables without relying on large sample approximations.

5 Must Know Facts For Your Next Test

1. Fisher's Exact Test calculates exact probabilities for each possible outcome of a contingency table rather than relying on asymptotic approximations.
2. It is particularly favored in studies with small sample sizes (often less than 20 observations), where traditional tests like the Chi-Squared Test may not be valid.
3. The test evaluates the null hypothesis that two categorical variables are independent, providing insights into their potential association.
4. Fisher's Exact Test is computationally intensive as it involves calculating hypergeometric distributions for all possible configurations of the table.
5. The result of Fisher's Exact Test yields a P-value that helps determine whether to reject or fail to reject the null hypothesis, indicating if there is a significant association.

Review Questions

• How does Fisher's Exact Test differ from the Chi-Squared Test when evaluating the independence of two categorical variables?
  • Fisher's Exact Test is specifically designed for small sample sizes and computes exact probabilities for each outcome, making it reliable even with limited data. In contrast, the Chi-Squared Test relies on larger sample approximations and may not be appropriate when expected frequencies are low. Therefore, while both tests evaluate independence, Fisher's Exact Test is preferred in situations where sample size limitations exist.
• Discuss the scenarios in which Fisher's Exact Test should be utilized instead of other statistical tests.
  • Fisher's Exact Test should be utilized in scenarios where sample sizes are small, typically when any expected cell count in a contingency table is below 5. This ensures that the assumptions underlying larger sample tests, like the Chi-Squared Test, are met. Additionally, it's appropriate when dealing with rare events or outcomes in categorical data, where accurate probability calculations are essential for valid conclusions.
• Evaluate how the results of Fisher's Exact Test can impact decision-making in research involving categorical data.
  • The results of Fisher's Exact Test provide critical insights into the relationship between categorical variables, influencing research conclusions and subsequent decision-making. A significant P-value suggests a nonrandom association between the variables, prompting further investigation or potential changes in practice. Conversely, a non-significant result may lead researchers to conclude that there is no evidence of association, impacting future studies and resource allocation based on those findings.

Related terms

Contingency Table: A table used to display the frequency distribution of variables, showing the relationship between two categorical variables.

Chi-Squared Test: A statistical test that assesses the goodness of fit between observed and expected frequencies in categorical data, often used as an alternative to Fisher's Exact Test when sample sizes are larger.

P-value: The probability of obtaining test results at least as extreme as the observed results, under the assumption that the null hypothesis is true.