Fixed and Random Effects

Introduction to Analysis-of-Variance Procedures

Fixed and Random Effects

The explanatory classification variables in an ANOVA design may represent fixed or random effects. The levels of a classification variable for a fixed effect give all the levels of interest, while the levels of a classification variable for a random effect are typically a subset of levels selected from a population of levels. The following are examples.

In a large drug trial, the levels that correspond to types of drugs are usually considered to comprise a fixed effect, but the levels corresponding to the various clinics where the drugs are administered comprise a random effect.
In agricultural experiments, it is common to declare locations (or plots) as random because the levels are chosen randomly from a large population of locations and you assume fertility to vary normally across locations.
In repeated-measures experiments with people or animals as subjects, subjects are declared random because they are selected from the larger population to which you want to generalize.

A typical assumption is that random effects have values drawn from a normally distributed random process with mean zero and common variance. Effects are declared random when the levels are randomly selected from a large population of possible levels. Inferences are made using only a few levels but can be generalized across the whole population of random effects levels.

The consequence of having random effects in your model is that some observations are no longer uncorrelated but instead have a covariance that depends on the variance of the random effect. In fact, a more general approach to random effect models is to model the covariance between observations.

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