How to Perform Fisher’s Exact Test in Python

Fisher’s Exact Test is used to determine whether or not there is a significant association between two categorical variables.

It is typically used as an alternative to the Chi-Square Test of Independence when one or more of the cell counts in a 2×2 table is less than 5. 

This tutorial explains how to perform Fisher’s Exact Test in Python.

Example: Fisher’s Exact Test in Python

Suppose we want to know whether or not gender is associated with political party preference at a particular college.

To explore this, we randomly poll 25 students on campus. The number of students who are Democrats or Republicans, based on gender, is shown in the table below:

To determine if there is a statistically significant association between gender and political party preference, we can use the following steps to perform Fisher’s Exact Test in Python:

Step 1: Create the data.

First, we will create a table to hold our data:

data = [[8, 4],
         [4, 9]]

Step 2: Perform Fisher’s Exact Test.

Next, we can perform Fisher’s Exact Test using the fisher_exact function from the SciPy library, which uses the following syntax:

fisher_exact(table, alternative=’two-sided’) 

where:

• table: A 2×2 contingency table
• alternative: Defines the alternative hypothesis. Default is ‘two-sided’, but you can also choose ‘less’ or ‘greater’ for one-sided tests.

The following code shows how to use this function in our specific example:

import scipy.stats as stats

print(stats.fisher_exact(data))

(4.5, 0.1152)

The p-value for the tests is 0.1152.

Fisher’s Exact Test uses the following null and alternative hypotheses:

• H₀: (null hypothesis) The two variables are independent.
• H₁: (alternative hypothesis) The two variables are not independent.

Since this p-value is not less than 0.05, we do not reject the null hypothesis.

Thus, we don’t have sufficient evidence to say that there is a significant association between gender and political party preference.

In other words, gender and political party preference are independent.