ABSTRACT

This chapter introduces many applications of nested factors in contemporary research tend to be analyzed by methods referred to variously as hierarchical, multi-level, or mixed-effects models, which build on and extend the classic ANOVA approach. It presents methods appropriate for multifactor designs where the factors are not crossed but nested, for example where the various levels of one factor appear in conjunction with only one level of the other factor. Factors having randomly selected levels are termed random factors, and the statistical models appropriate for analyzing experiments based on such factors are termed random-effects models. When we move to designs involving two independent variables, all three conceivable variations on the presence of random factors are possible. With such multiple-factor designs, a somewhat counterintuitive result occurs in the impact of the random factor on the expected mean square for the various effects.