# Fisher Exact Test Calculator

Run Fisher exact test for a 2 x 2 contingency table with exact one-sided or two-sided p-values

> Canonical page: https://elysiatools.com/en/tools/fisher-exact-test-calculator

- **Category:** Math & Numbers

- **Keywords:** fisher exact test, 2x2 table, contingency table, exact p value, statistics, calculator

## Overview

The Fisher Exact Test Calculator provides a precise statistical analysis for 2x2 contingency tables, determining the significance of the association between two categorical variables. Unlike the Chi-square test, this tool calculates exact p-values, making it the standard choice for small sample sizes where asymptotic approximations are unreliable.

## Inputs

- **Cell A** (number)
- **Cell B** (number)
- **Cell C** (number)
- **Cell D** (number)
- **Alternative Hypothesis** (select)
- **Alpha** (number)
- **Decimal Places** (number)

## When to use

- When analyzing categorical data in a 2x2 contingency table with small sample sizes.
- When any expected cell frequency in a contingency table is less than five.
- When you need an exact p-value rather than an approximation for hypothesis testing.

## How it works

- Enter the observed frequencies into the four cells (A, B, C, and D) of the 2x2 contingency table.
- Select the alternative hypothesis (two-sided, greater than, or less than) and set your significance level (alpha).
- The tool calculates the probability of the observed distribution and more extreme cases using the hypergeometric distribution.
- Review the resulting p-value and odds ratio to determine if the null hypothesis should be rejected based on your alpha.

## Use cases

- Comparing the success rate of two different medical treatments in a small clinical trial.
- Analyzing the relationship between a specific gene mutation and the presence of a rare disease.
- Evaluating the effectiveness of two different marketing A/B test variations with low conversion counts.

## Frequently asked questions

### What is the difference between Fisher's Exact Test and Chi-square?

Fisher's test provides an exact p-value based on the hypergeometric distribution, while Chi-square uses an approximation that is often inaccurate for small samples.

### Can I use this for tables larger than 2x2?

No, this specific calculator is designed exclusively for 2x2 contingency tables.

### What does the 'Greater Than' alternative hypothesis test?

It tests if the proportion of successes in the first group is significantly larger than the proportion in the second group.

### What is the significance of the Odds Ratio?

The odds ratio quantifies the strength of the association between the two categorical variables, indicating how much more likely an outcome is in one group versus another.

### What is a typical Alpha value for this test?

Most researchers use 0.05 as the standard threshold for determining statistical significance.

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