Fisher's Exact Test

Definition

Fisher's Exact Test is a statistical method used to analyze the relationship between two categorical variables, particularly when the sample size is small. It is commonly employed in the context of hypothesis testing to determine whether there is a significant association between two variables.

5 Must Know Facts For Your Next Test

1. Fisher's Exact Test is particularly useful when the expected cell frequencies in a contingency table are small, as it provides a more accurate p-value compared to the Chi-Square Test of Independence.
2. The test calculates the exact probability of obtaining the observed or more extreme frequencies in the contingency table, assuming the null hypothesis of independence is true.
3. Fisher's Exact Test is based on the hypergeometric distribution, which models the probability of obtaining a specific arrangement of the data in the contingency table.
4. The test is often used in the analysis of 2x2 contingency tables, but it can be extended to larger tables as well.
5. Fisher's Exact Test is a non-parametric test, meaning it does not require assumptions about the underlying distribution of the data, making it a robust alternative to the Chi-Square Test of Independence.

Review Questions

• Explain the purpose and application of Fisher's Exact Test in the context of the Hypergeometric Distribution.
  • Fisher's Exact Test is closely related to the Hypergeometric Distribution, as it is used to analyze the relationship between two categorical variables when the sample size is small. The Hypergeometric Distribution models the probability of obtaining a specific arrangement of data in a contingency table, and Fisher's Exact Test calculates the exact probability of observing the given or more extreme frequencies in the table, assuming the null hypothesis of independence is true. This makes Fisher's Exact Test particularly useful when the expected cell frequencies are small, as it provides a more accurate p-value compared to the Chi-Square Test of Independence, which relies on asymptotic approximations.
• Describe how Fisher's Exact Test can be used in the context of the Chi-Square Test of Independence, and explain the advantages of using Fisher's Exact Test in this scenario.
  • The Chi-Square Test of Independence is a commonly used method for analyzing the relationship between two categorical variables, but it relies on the assumption that the expected cell frequencies in the contingency table are sufficiently large. In situations where the sample size is small and the expected cell frequencies are small, the Chi-Square Test may not be appropriate, as it can lead to inaccurate p-values. In these cases, Fisher's Exact Test can be used as an alternative, as it calculates the exact probability of observing the given or more extreme frequencies in the contingency table, without relying on asymptotic approximations. This makes Fisher's Exact Test a more robust and accurate method for assessing the independence of two categorical variables, particularly when the sample size is limited.
• Analyze the key differences and similarities between Fisher's Exact Test and the Chi-Square Test of Independence, and explain the factors that would determine which test is more appropriate to use in a given scenario.
  • The primary difference between Fisher's Exact Test and the Chi-Square Test of Independence is the underlying statistical approach. Fisher's Exact Test calculates the exact probability of observing the given or more extreme frequencies in a contingency table, based on the Hypergeometric Distribution, while the Chi-Square Test relies on asymptotic approximations and the assumption of large expected cell frequencies. This makes Fisher's Exact Test more appropriate for small sample sizes and situations where the expected cell frequencies are small, as it provides a more accurate p-value. However, the Chi-Square Test may be preferred when the sample size is larger, as it is generally more computationally efficient. The choice between the two tests ultimately depends on the specific characteristics of the data, such as the sample size, the expected cell frequencies, and the desired level of accuracy in the statistical analysis.

Related terms

Hypergeometric Distribution:

The hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement.

Chi-Square Test of Independence:

The Chi-Square Test of Independence is a statistical test used to determine whether two categorical variables are independent or related.

Contingency Table:

A contingency table is a tabular format used to display the frequency distribution of two or more variables, typically used in statistical analysis to investigate the relationship between categorical variables.