Automating the analysis of variance of orthogonal designs

A new algorithm is presented which for the wide class of orthogonal designs is capable of deducing the appropriate analysis of variance from the design only. As a consequence the use of a model equation for specifying the analysis becomes dispensable. The proposed approach can simplify the analysis of complex models with iterative crossing and nesting of factors, where treatment factors have fixed and plot factors have random effects. An implementation is described and its use is illustrated with several examples.