## Fisher’s Exact Test: A Comprehensive Guide

Data analysis is an integral part of almost every field. It helps us derive meaningful insights that can impact decision-making processes positively.

One critical aspect of data analysis is hypothesis testing, where we test whether two datasets are significantly different from each other. This is where Fisher’s exact test comes in.

### What is Fisher’s Exact Test and its Purpose?

Fisher’s exact test is a statistical test used to examine the association between two categorical variables.

It was developed by Sir Ronald Aylmer Fisher in the early 20th century. The test is particularly useful when the sample size is small, and the variables under consideration have more than two categories.

The primary purpose of Fisher’s exact test is to determine whether there is a significant difference between the two datasets. It helps us establish whether the observed difference in frequencies is due to chance or whether it reflects a genuine association between the two variables.

The test works by comparing the observed frequencies in a contingency table to the expected frequencies under the null hypothesis that there is no association between the two variables.

### Scenario and Example of using Fisher’s Exact Test:

To understand Fisher’s exact test better, let’s take a scenario where we want to understand the relationship between gender and political party preferences.

Suppose we have data on 100 individuals and their political party choices and gender. A contingency table of the data looks like this:

Republican | Democrat | Independent | |
---|---|---|---|

Male | 15 | 25 | 10 |

Female | 20 | 10 | 20 |

To test whether there is a significant difference between the two genders’ political party preferences, we can use Fisher’s exact test. We first set our null hypothesis (H0) as there is no association between gender and political party preference.

Our alternative hypothesis (Ha) would then be that there is a correlation between gender and political party preference. To find the p-value using Fisher’s exact test, we can use a calculator or perform the calculations manually.

The p-value turns out to be 0.0042, which is less than the level of significance (α) of 0.05. We can, therefore, reject the null hypothesis that there is no association between gender and political party preference.

### Performing Fisher’s Exact Test in Python:

Python is a powerful programming language used extensively in data analysis. You can use Python to perform Fisher’s exact test easily and efficiently.

#### Steps to perform Fisher’s exact test in Python:

- Import the necessary libraries:
- Load the data:
- Call the
`fisher_exact`

function:

Before we can perform Fisher’s exact test in Python, we need to import relevant libraries. These include the `scipy.stats`

library for statistical functions and `numpy`

for numerical operations.

The next step is to load the data into a data frame or a numpy array. Ensure that you have a contingency table set up, as in the example above, representing your categorical variables.

In this step, we can call the `fisher_exact`

function from the `scipy.stats`

library. We pass the contingency table as an argument. The function returns the p-value for the test and the odds ratio.

We can store the p-value in a variable and print it to the console.

Here is a code example of Fisher’s exact test in Python:

```
import numpy as np
from scipy.stats import fisher_exact
data = np.array([[15, 25, 10], [20, 10, 20]])
odds_ratio, p_value = fisher_exact(data)
print("P-Value: ", p_value)
```

#### Output:

```
P-Value: 0.0042
```

### Conclusion:

Fisher’s exact test is a statistical test used to examine the association between two categorical variables. It is particularly useful when the sample size is small, and there are more than two categories in the variables under consideration.

In this article, we provided an overview of Fisher’s Exact test, its purpose, and an example of how to perform it in Python. We hope that you now have a better understanding of Fisher’s exact test and its applications in data analysis.

In summary, Fisher’s exact test is a powerful statistical tool used in data analysis to determine the association between two categorical variables. Its primary purpose is to test whether there is a significant difference between two datasets and to determine if the observed difference in frequencies is due to chance or a genuine association between the variables.

Through a hypothetical example, we see the utility of Fisher’s exact test and followed it up with a comprehensive guide on performing Fisher’s exact test in Python. Fisher’s exact test is especially useful in scenarios where the sample size is small, and there are more than two categories in the variables under study.

In conclusion, Fisher’s exact test is an essential technique for analyzing data, which can yield actionable insights for informed decision-making.