Class ANOVAFactorial performs an analysis for an n-way classification design with balanced data. For balanced data, here must be an equal number of responses in each cell of the n-way layout. The effects are assumed to be fixed effects. The model is an extension of the two-way model to include n factors. The interactions (two-way, three-way, up to n-way) can be included in the model, or some of the higher-way interactions can be pooled into error. The ModelOrder property specifies the number of factors to be included in the highest-way interaction. For example, if three-way and higher-way interactions are to be pooled into error, set ModelOrder = 2. (By default, ModelOrder = nSubscripts - 1 with the last subscript being the error subscript.) Pure indicates there are repeated responses within the n-way cell; Pooled indicates otherwise.

Class ANOVAFactorial requires the responses as input into a single vector y in lexicographical order, so that the response subscript associated with the first factor varies least rapidly, followed by the subscript associated with the second factor, and so forth. Hemmerle (1967, Chapter 5) discusses the computational method.