The relationship of ANOVA models with random effects and repeated measurement designs

Understanding ANOVA models is often difficult because of the large amount o f different experimental designs presented in applied textbooks. This artic le shows how different experimental designs arise out of the variation of t hree basic distinctions: block versus treatment factors, fixed versus rando m factors, and crossed versus nested factors. Once it is understood how eac h distinction influences the statistical analysis, the amount of experiment al designs can be considerably reduced, because sometimes seemingly differe nt experimental designs are essentially equivalent. This is shown by an exa mple comparing a two-way analysis of variance model to a three-factor parti ally nested design Furthermore, the way each distinction influences the sta tistical analysis of an experimental design can simplify the computational effort of the analysis because virtually every basic ANOVA procedure implem ented in common statistical software packages can be used to fit more compl ex ANOVA models that are usually analyzed using special computer modules.