Teaching Design of Experiments using Hasse diagrams

Hasse diagrams provide a principled means for visualizing the structure of statistical designs constructed by crossing and nesting of experimental factors. They have long been applied for automated construction of linear models and their associated linear subspaces for complex designs. Here, we argue that they could also provide a central component for planning and teaching introductory or service courses in experimental design. Specifically, we show how Hasse diagrams allow constructing most elementary designs and finding many of their properties, such as degrees of freedom, error strata, experimental units and denominators for F-tests. Linear (mixed) models for analysis directly correspond to the diagrams, which facilitates both defining a model and specifying it in statistical software. We demonstrate how instructors can seamlessly use Hasse diagrams to construct designs by combining simple unit- and treatment structures, identify pseudo-replication, and discuss a design's randomization, unit-treatment versus treatment-treatment interactions, or complete confounding. These features commend Hasse diagrams as a powerful tool for unifying ideas and concepts.