Basic Ideas of Variance Components Analysis
Experimentation is sometimes mistakenly thought to involve only the manipulation of levels of the independent variables and the observation of subsequent responses on the dependent variables. Independent variables whose levels are determined or set by the experimenter are said to have fixed effects.
There is a second class of effects, however, which is often of great interest to the researcher. Random effects are classification effects where the levels of the effects are assumed to be randomly selected from an infinite population of possible levels. Many independent variables of research interest are not fully amenable to experimental manipulation, but nevertheless can be studied by considering them to have random effects.
For example, the genetic makeup of individual members of a species cannot at present be (fully) experimentally manipulated, yet it is of great interest to the geneticist to assess the genetic contribution to individual variation on outcomes such as health, behavioral characteristics, etc. As another example, a manufacturer might want to estimate the components of variation in the characteristics of a product for a random sample of machines operated by a random sample of operators. The statistical analysis of random effects is accomplished by using the random effects model if all of the independent variables are assumed to have random effects, or by using the mixed model if some of the independent variables are assumed to have random effects and other independent variables are assumed to have fixed effects. The Variance Components and Mixed Model ANOVA/ANCOVA module provides a comprehensive set of techniques for analyzing research designs that include random effects.