A **fisher exact test calculator** is a **statistical tool** used to analyze **contingency tables**, particularly when **sample sizes** are small. Developed by **R.A. Fisher**, this test is especially useful when the **chi-square test assumptions** are not met.

The calculator is particularly valuable in fields such as **biology**, **medicine**, and **social sciences**, where researchers often work with small sample sizes or rare events. It provides a more accurate **p-value** than the chi-square test when expected frequencies are low, making it a go-to method for analyzing **2×2 contingency tables** in such scenarios.

## Fisher Exact Test Calculation Chart

Observed Data | Column 1 | Column 2 | Row Total |
---|---|---|---|

Row 1 | a | b | a + b |

Row 2 | c | d | c + d |

Column Total | a + c | b + d | N |

Where:

a, b, c, dare the observed frequenciesNis the total sample size (a + b + c + d)

Calculation Step | Formula / Description |
---|---|

1. Calculate p | p = (a+b)!(c+d)!(a+c)!(b+d)! / (N!a!b!c!d!) |

2. Sum p-values | Sum p for all tables with fixed marginals and p ≤ observed p |

3. Interpret | If sum ≤ significance level, reject null hypothesis |

## Fisher Exact Test Formula

**p = (a+b)!(c+d)!(a+c)!(b+d)! / (N!a!b!c!d!)**

Where:

a, b, c, dare the cell frequenciesNis the total sample size!denotesfactorial

Treatment | Recovered | Not Recovered | Total |
---|---|---|---|

Drug | 8 (a) | 2 (b) | 10 |

Placebo | 3 (c) | 7 (d) | 10 |

Total | 11 | 9 | 20 |

`Applying the formula: `**p = (10!10!11!9!) / (20!8!2!3!7!)**

The **Fisher Exact Test** calculates the probability of obtaining the observed (or more extreme) frequencies in a **2×2 contingency table**, given the row and column totals.

## How do you calculate Fisher’s exact test?

Calculating **Fisher’s exact test** involves several steps:

**Arrange the data** in a 2×2 contingency table.

**Calculate the p-value** using the formula mentioned earlier.

**Sum the p-values** for all possible tables with the same marginal totals that are as extreme or more extreme than the observed table.

**Compare the sum** to the chosen significance level.

Treatment | Recovered | Not Recovered |
---|---|---|

Drug | 8 | 2 |

Placebo | 3 | 7 |

**Step 1**: The data is already in a 2×2 table.

**Step 2**: Calculate p for this table using the formula (result from previous calculation).

**Step 3**: Calculate p for all possible more extreme tables with the same marginals. In this case, there’s only one more extreme table:

Treatment | Recovered | Not Recovered |
---|---|---|

Drug | 9 | 1 |

Placebo | 2 | 8 |

Calculate p for this table and add it to the p from step 2.

**Step 4**: If the sum of p-values is less than the chosen significance level (e.g., **0.05**), we reject the **null hypothesis** of no association between the treatment and recovery.