## 11.6 Goodness-of-fit tests

This tutorial is under construction, and will not be covered in 2022

In this tutorial, we continue to learn how to test hypotheses about a categorical variable.

We previously learned how to test a hypothesis about frequencies or proportions when the variable has only two categories of interest, i.e. success and failure (a binary variable). We used a binomial test for this purpose. It is important to note, however, that even in cases where the variable has more than two categories (e.g. hair colour: brown, black, blonde, red), one can define a particular category (e.g. red hair) as a “success”, and the remaining categories as failures, in which case we have simplified our variable to a binary categorical variable.

For testing hypotheses about frequencies or proportions when there are more than two categories, we use goodness of fit (GOF) tests. In general, these types of test evaluate how well an observed discrete frequency (or probability) distribution fits some hypothesized frequency distribution. We’ll demonstrate this next.