A Recent Study on the Graeco-Latin Square and Hyper Graeco-Latin Square Designs

A Latin square model can simultaneously control two sources of nuisance variability. As an experimental design model, the Graeco-Latin square is an extension of a Latin square and can simultaneously control three sources of nuisance variability. The first mentioning of the Graeco-Latin square was in 1782. The following aspects of this model will be discussed: A brief history, estimation and ANOVA, use for the analysis of experimental data (example with R code given), model generation and a test for non-additivity. An R example of the Hyper Graeco-Latin square model, which extends the Graeco-Latin square to controlling four sources of nuisance variability, will also be discussed.