##
Overview
Section* *

In this course, we have finished the first exam and we are now moving into a new set of materials. You need to pay extra attention to this section. Why?

First, this is a rather lengthy section with a lot of information and second, we are now going to introduce random effects into our models. So, while a lot of the rules and the ideas that you have learned in the first part of the course hold, there are some different tweaks along the way and some new ways of thinking about things. From this point on in this course, we will be dealing with random and fixed effects.

#### Random Effects and Introduction to Mixed Models

In our discussion of Treatment Designs to this point we have been making an unstated, but important, assumption about the nature of the treatments. We have assumed that the levels of the treatments were chosen intentionally by the researcher to be of specific interest. The scope of inference in this situation is limited to the specific levels used in the study. However, this is not always the case. Sometimes, treatment levels may be a (random) sample of possible levels, and the scope of inference is to a larger population of possible levels.

Going back to the ‘Working Hypothesis’ of Lesson 1, it is here that the stage is set to determine the purpose of the study. If it is clear that the researcher is interested in comparing specific, chosen levels of treatment, that treatment is a **fixed effect**. On the other hand, if the levels of the treatment are a sample of a larger population of possible levels, then the treatment is a **random effect**.

## Objectives

- Extending the treatment design to include random effects
- Use of random effects models
- Combining fixed and random effects in the mixed model