Categorical Variables are used in ANOMA, ANOVA, with Proportions, and in the Chi-Square Tests for Independence and Goodness of Fit. Categorical Variables are also known as "Nominal" (named) Variables and "Attributes" Variables.
The concept can be confusing, because the values of a Categorical Variable are not numbers, but names of categories. The numbers associated with Categorical Variables come from counts of the data values within a named category. Here's how it works:
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.