Analysis of variance (ANOVA) is the generalization of a t-test to more
than two groups. There are different kinds of ANOVA: one-way, with
just a single factor, and two- or multiway, with two or more factors,
and main- and interaction-effects models (see Chapter 10). Here, we
present a one-way ANOVA and introduce the concept of random effects
along the way. In random-effects models, a set of effects (e.g., group
means) is constrained to come from some distribution, which is most
often a normal, although it may be a Bernoulli (see Chapter 20), a Poisson
(see Chapter 21) or yet another distribution. In this chapter, we will first
generate and analyze a fixed-effects and then a random-effects ANOVA
data set. In Chapters 12, 16, and 19–21, we will focus on mixed models,
i.e., those containing both fixed and random effects. As a motivating
example for this chapter, we assume that we measured snout–vent length