What type of data requires the use of the Fisher's Exact test?

The Fisher's Exact test is specifically designed to evaluate the significance of the association between two categorical variables in a contingency table, particularly when sample sizes are small. This makes it particularly suitable for analyzing nominal data, which consists of categories that do not have a specific order or ranking. For example, outcomes such as gender, color, or type of treatment are categorical in nature, making the Fisher's Exact test an appropriate statistical tool in these situations.

When dealing with nominal data, one might encounter a 2x2 contingency table, where the Fisher's Exact test can precisely assess whether the proportions of one category differ significantly from those of another category. In scenarios where sample sizes are insufficient for the assumptions required by the chi-squared test, Fisher’s Exact test provides a more valid alternative.

In contrast, ordinal data involves a clear ordering or ranking of categories and typically uses different statistical tests more suited to ordered datasets. Continuous data is on a scale and represents values that can be measured, making it inappropriate for Fisher's Exact test, and interval data, while it can also be measured, typically requires different analysis methods like t-tests or ANOVA for comparisons. Thus, nominal data is the correct type for the application of the Fisher's Exact test.