Fixed, Random, and Mixed Effects

General Notes

What most people recognize as ANOVA is based on a fixed effects model. The differences between the fixed effects model and the random effects model include:

the hypothesis being tested
the way that the F-ratios are calculated to test for significance of the terms
some of the assumptions behind the ANOVA model

The hypothesis for a fixed effects model is based on finding differences in means between levels of a factor. The hypothesis for a random effects model is based on the significance of the variance component contributed by the factor to the overall variance. These are two very different types of hypotheses.

The denominator used to test a factor for significance in the fixed effects model is always the Mean Square Error (MSE) term. The denominator used to test a factor for significance in the random and mixed effects models is determined by the EMS table. The structure of the EMS table should be determined when the experiment is being designed, and is based on the hypotheses/goals of the experiment.

See Variance Components.

Assumptions

The random effects model assumes that the items within a factor are randomly drawn from a larger population of such items, and are representative of that population.

In a fixed effects model, one assumption - homoskedasticity - is that the variances between levels of a factor are equal.

References

See text on Variance Components by Searle.