The Relationship of ANOVA Models with Random Effects and Repeated Measurement Designs

Abstract

Understanding ANOVA models is often difficult because of the large amount of different experimental designs presented in applied textbooks.This article shows how different experimental designs arise out of the variation of three basic distinctions: block versus treatment factors, fixed versus random factors, and crossed versus nested factors.Once it is understood how each distinction influences the statistical analysis, the amount of experimental designs can be considerably reduced, because sometimes seemingly different experimental designs are essentially equivalent.This is shown by an example comparing a two-way analysis of variance model to a three-factor partially nested design.Furthermore, the way each distinction influences the statistical analysis of an experimental design can simplify the computational effort of the analysis because virtually every basic ANOVA procedure implemented in common statistical software packages can be used to fit more complex ANOVA models that are usually analyzed using special computer modules.