Statistics Definitions > Fisher’s Exact Test of Independence

What are nominal variables?

What is a contingency table?

In order to understand Fisher’s, you may want to read these articles first:

## What is Fisher’s Exact Test of Independence?

Fisher’s Exact Test of Independence is a statistical test used when you have two nominal variables and want to find out if **proportions **for one nominal variable are different among values of the other nominal variable. For experiments with small numbers of participants (under around 1,000), Fisher’s is more accurate than the chi-square test or G-test.

Unlike other statistical tests, there isn’t a formula for Fisher’s. To get a result for this test, calculate the probability of getting the observed data using the null hypothesis that the proportions are the same for both sets.

**Fisher’s Exact Test of Independence example situation:
**You are studying if certain treatments for skin cancer lead to good outcomes. The first nominal variable is the treatment: some patients are given drug X and others are given drug Y. The second nominal variable is the outcome: patients are cured of cancer, or they are not. When you complete the study of 50 patients, you find that the percentage of patients who were cured and took drug X is much higher than patients who took drug Y. Fisher’s Exact Test of Independence will tell you if your results are statistically significant.

## Calculation

Fisher’s Exact Test of Independence uses a contingency table to display the different outcomes for an experiment. Although it’s possible to calculate it by hand (you can find the procedure here — scroll down to “Fisher Exact Probability Test: Logic and Procedure”), why would you want to? For more than a handful of entries, the calculations can be very tedious.

**Note on one sided and two sided tests**: the one-sided Fisher’s tests if a result is greater than or less than a certain amount. The two sided Fisher’s tests if a result is different from a certain proportion. In most cases, you’ll probably use a two-sided test.

You can find an **online calculator for Fisher’s Exact test** here. It’s also possible to calculate it in Microsoft Excel. Download this Excel worksheet and replace the entries with your data.