Fisher's Exact Test

Definition

Fisher's Exact Test is a statistical method used to determine if there are nonrandom associations between two categorical variables in a contingency table, particularly when sample sizes are small. This test is especially useful when the assumptions for other tests, like the Chi-square test, are not met due to low expected frequencies. It computes the exact probability of observing the data given the null hypothesis of independence between the variables.

5 Must Know Facts For Your Next Test

1. Fisher's Exact Test is often employed in clinical trials and biomedical research where sample sizes can be limited, making it a go-to method for analyzing small datasets.
2. The test calculates the probability of obtaining a distribution of values as extreme or more extreme than what was observed under the null hypothesis.
3. It works by enumerating all possible configurations of a contingency table and calculating their probabilities, ensuring an exact result rather than an approximation.
4. While Fisher's Exact Test is primarily used for 2x2 tables, it can be extended to larger tables using methods like the hypergeometric distribution.
5. One key advantage is that it does not require the assumption of normality or large sample sizes, making it versatile for many scenarios.

Review Questions

• How does Fisher's Exact Test differ from the Chi-Square test in terms of application and assumptions?
  • Fisher's Exact Test is specifically designed for small sample sizes and situations where the assumptions of the Chi-Square test, such as having a sufficient expected frequency in each cell, do not hold. The Chi-Square test relies on approximate distributions and larger sample sizes to yield reliable results, whereas Fisher's Exact Test calculates exact probabilities without these assumptions. Therefore, in cases with sparse data or small samples, Fisher's Exact Test is preferred.
• Explain how Fisher's Exact Test can provide insights into the independence of two categorical variables in a contingency table.
  • Fisher's Exact Test assesses whether there is a statistically significant association between two categorical variables by evaluating the distribution of data within a contingency table. It does this by calculating the probability of observing the data under the assumption that the two variables are independent. If the resulting p-value from the test is below a pre-defined significance level (commonly 0.05), it suggests that the variables are likely associated rather than independent.
• Evaluate the significance of Fisher's Exact Test in modern statistical analysis, especially in fields with limited data availability.
  • Fisher's Exact Test holds substantial significance in modern statistical analysis, particularly in fields such as medicine and social sciences where datasets can be limited due to ethical or practical constraints. Its ability to provide exact p-values allows researchers to draw reliable conclusions even when sample sizes are small or unevenly distributed. This reliability has made it invaluable in clinical trials and studies involving rare events, where traditional tests might fail to provide valid results. As data analysis continues to evolve, understanding and applying Fisher's Exact Test ensures that researchers can maintain statistical rigor in challenging scenarios.

Related terms

Contingency Table:

A type of table that displays the frequency distribution of variables, allowing for the analysis of relationships between categorical variables.

Null Hypothesis:

A general statement that there is no effect or no difference, used as a starting point for statistical testing.

Chi-Square Test: A statistical test used to determine if there is a significant association between categorical variables, applicable when sample sizes are sufficiently large.