By Dan Adrian (Grand Valley State University)
Students routinely tell me that they find visual aids helpful. And my favorite visual aids when teaching Design of Experiments are the factor diagrams from George Cobb’s textbook “Introduction to Design and Analysis of Experiments”. These diagrams illustrate the factors in a design, or associated ANOVA model, as different ways of partitioning the data table. The diagrams make the structure of model/design much more explicit than algebraic expressions for ANOVA models, which can be introduced later. Beyond introducing model/design structure, Cobb also uses factor diagrams as a general framework through which to decompose response values into a sum of estimated effects, find degrees of freedom, and assemble the ANOVA table for completely randomized, complete block, Latin square, and split plot designs.