What is the difference between fixed and random factors?

Categorical factors can be either fixed or random. Usually, if the investigator controls the levels of a factor, then the factor is fixed. Conversely, if the investigator randomly sampled the levels of a factor from a population, then the factor is random.

Suppose you have a factor called "operator," and it has three levels. If you intentionally select these three operators and want your results to apply to only these operators, then the factor is fixed. However, if you randomly sample three operators from a larger number of operators, and you want your results to apply to all operators, then the factor is random.