Path: Selector > Categorical Data > Two Categories > Association > Fisher Exact Test
Introduction to Fisher Exact Test
The Fisher Exact Test is a statistical method used to determine whether there is a significant association between two categorical variables, particularly in small sample sizes. This test is commonly used in fields such as medicine, biology, and social sciences to test hypotheses about the relationships between categorical variables in contingency tables. By selecting “Fisher Exact Test” under the “Categorical Data,” “Two Categories,” and “Association” categories, you are focusing on a method that helps to evaluate the association between two categorical variables based on small or sparse sample data.
How Fisher Exact Test Fits the Selection Categories
Categorical Data: Categorical data represents characteristics or attributes that can be divided into different groups or categories, such as gender, race, or treatment groups. The Fisher Exact Test is particularly suitable for categorical data as it compares the observed frequencies of the categories.
Two Categories: When dealing with two categorical variables, the Fisher Exact Test allows you to assess the association between the two variables by comparing the observed frequencies in each category to the expected frequencies under the null hypothesis.
Association: The primary goal of the Fisher Exact Test is to determine whether there is a significant association between two categorical variables, especially in cases where the sample size is too small for the Chi-Square test to be reliable.
Key Concepts in Fisher Exact Test
Exact Probability: Unlike the Chi-Square test, which relies on an approximation, the Fisher Exact Test calculates the exact probability of observing the data assuming the null hypothesis is true. This makes it particularly useful for small sample sizes or when the expected frequencies are very low.
Contingency Table: A contingency table is used to summarize the relationship between two categorical variables. For a 2×2 table, the Fisher Exact Test is commonly applied. The table structure is as follows:
| Variable B: Category 1 | Variable B: Category 2 | |
|---|---|---|
| Variable A: Category 1 | a | b |
| Variable A: Category 2 | c | d |
Where:
- a, b, c, and d represent the frequencies of the observed categories.
Calculating the Test Statistic: The Fisher Exact Test calculates the probability of obtaining the observed frequencies (and those more extreme) under the null hypothesis using the hypergeometric distribution. The formula for the exact probability (p) is:
p = ( (a + b)! (c + d)! (a + c)! (b + d)! ) / ( n! a! b! c! d! )
Where:
- n is the total number of observations (a + b + c + d).
P-Value: The p-value helps determine the significance of the test result. It is compared against a chosen significance level (α), usually 0.05, to decide whether to reject the null hypothesis. A small p-value (typically < 0.05) indicates that there is a significant association between the categorical variables.
Assumptions of Fisher Exact Test
The Fisher Exact Test relies on the following assumptions:
- The data should be categorical.
- The observations should be independent of each other.
- The sample size should be small, or the expected frequencies should be low.
Using Fisher Exact Test in Excel
Excel does not have a built-in function for the Fisher Exact Test, but you can use the FisherExactTest function available in the Real Statistics add-in or other statistical software. Here are the steps to perform a Fisher Exact Test using the Real Statistics add-in in Excel:
- Prepare your data: Ensure your data is organized in a 2×2 contingency table format.
- Install the Real Statistics add-in: Download and install the Real Statistics add-in from the Real Statistics website.
- Use the Real Statistics add-in:
- Go to the “Add-Ins” tab and select “Real Statistics.”
- Choose “Fisher Exact Test” from the menu.
- Input the data ranges: In the Fisher Exact Test dialog box, input the range for your contingency table data.
- Run the analysis: Click “OK” to generate the Fisher Exact Test output, which will include the exact p-value.
Alternatively, you can use other statistical software such as R, Python, or online calculators to perform the Fisher Exact Test.
Interpretation of Results
Once you have the Fisher Exact Test output, you can interpret the results by examining the p-value:
- P-Value: A small p-value (typically < 0.05) suggests that there is a significant association between the two categorical variables.
- Exact Probability: The exact probability calculated by the test provides a precise measure of the likelihood of observing the data under the null hypothesis.
Conclusion
The Fisher Exact Test is a powerful tool for testing the association between two categorical variables, especially in small sample sizes or when the expected frequencies are low. By understanding the key concepts, assumptions, and how to perform the test in Excel using add-ins, you can effectively use this method to evaluate relationships between categorical variables. Mastering the Fisher Exact Test enhances your ability to make data-driven decisions and draw meaningful conclusions from your data. Although Excel does not have a built-in function for the Fisher Exact Test, add-ins and other statistical software provide accessible platforms for performing this analysis.
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Last Modified: 06/13/2024