# Lesson 13: Experiments with Random Factors

**Introduction**

Throughout most parts of this course we have discussed experiments with **fixed factors**. That is, the levels used for the factors are those of interest by the experimenter and the inference made is confined to those specific levels. However, when factor levels are chosen at random from a larger population of potential levels, the factor is called a **random factor**. In this case, the statistical inference applies to the whole population of levels. **Random factor** models have many industrial applications including measurement system studies.

**Learning Objectives & Outcomes**

- Understanding the concept of random effect
- Getting familiar with random effect models and components of variance in each model
- Learning how to deal with models containing two random factors
- Getting familiar with how to analyze experiments where one of the factors is fixed and the other one is random
- Finding the expected mean squares using a simple algorithm